begin shift to nim code base

lang/demo/cycgrp.no

@@ -0,0 +1,103 @@
+/*
+Type Traits (TTrait)
+Operation Traits (OTrait)
+Types (implement TTraits)
+Operations on types (implement OTraits)
+*/
+
+trait QuotientRemainder<T: Any>:
+	proc quotient(a: T, b: T): T
+	proc remainder(a: T, b: T): T
+
+induce QuotientRemainder on Self: Any having
+						   `+`<Self>: BinOp | Invertible | UniqueIdentity,
+						   `<`<Self>: POrder, // NOTE: PartialOrders implement BinOp
+						   `==`<Self>: EqRel -> // NOTE: EqRels implement BinOp
+	// `let` is a macro that replaces all instances following code's
+	// AST with whatever values were defined via alias
+	// (it does NOT change scope at all)
+	with (
+		// define aliases for the inverse of an element as both a
+		// prefixed unary operation and a infix binary operation
+		preunary `-`(a: Self) -> +.inverse(a) // -a = +(inverse(a))
+		binop `-`(a: Self, b: Self) -> a + +.inverse(b) // a - b = a +(inverse(b))
+		// define aliases for <= by simply inducing <= from < and = on Self
+		binop `<=`(a: Self, b: Self) -> a == b or a < b
+	):
+		// NOTE: any proc for a trait can be overriden, the standard definitions
+		// NOTE: are just the standard "induced" definitions
+		
+		proc quotient(a: Self, b: Self): Self ->
+			var quotient: Integer = 1
+			alias delta -> b
+			while not (delta <= b):
+				delta = delta - b
+				quotient++
+			return quotient
+
+		// NOTE: assumes a is passed by value not by reference
+		proc remainder(a: Self, b: Self): Self ->
+			alias delta -> a // compiler alias
+			while not (delta <= b):
+				delta = delta - b
+			return delta
+
+// define the standard induce of Modulo via QuotientRemainder
+induce Modulo on T: QuotientRemainder ->
+	binop mod(a: T, b: T): T -> T.remainder(a, b)
+
+// NOTE: the Slicable trait allow us to take slices ie `1..5`
+type CycGrp<T: Modulo | Slicable having `+`<T>: BinOp|Invertible|UniqueIdentity>: Group<T> ->
+	// intrinsic variables
+	intrinsic modulus: T
+	intrinsic elements : Set<T>
+
+	structure(modulus: T) ->
+		self.modulus = modulus
+		// the following line is a generalised implementation of `1..(self.modulus-1)`
+		self.elements = (self.modulus + +.inverse(self.modulus))..(self.modulus + +.inverse(+.identity))
+
+	// "functors" allow one type to be represented as another type
+	// aka functors == typecasts
+	functor(value: T) -> value mod self.modulus
+
+	
+
+
+
+
+/* My attempt at formalising rings and fields in Noether
+ * NOTE: the following traits are "formed" from a specific structure
+ * NOTE: they have properties (`prop`) which are just aliases to 
+ * NOTE: the structure that formed them
+ */
+trait Magma<T: Any> on (SET: Set<T>, ACTION: BinOp<T>) ->
+	prop SET -> SET
+	prop ACTION -> ACTION
+	
+trait SemiGroup<T: Any> 
+		on (M: Magma<T>) 
+		having M#ACTION: Associative ->
+	inherit M#SET, M#ACTION
+
+trait Group<T: Any> 
+		on (SG: SemiGroup<T>)
+		having SG#ACTION: UniqueIdentity | Invertible ->
+	inherit SG#SET, SG#ACTION
+	
+trait Ring<T: Any> 
+		on (SET: Set<T>, ADD: BinOp<T>, MUL: BinOp<T>)
+		having (SET, ADD) : Group<T>,
+			   (SET, MUL) : SemiGroup<T>,
+			   (ADD, MUL) : Distributive ->
+	prop SET -> SET
+	prop ADD -> ADD
+	prop MUL -> MUL
+
+/*
+ * Notation: (`->` as `return`)
+ * x() -> expr 
+ * // same as:
+ * x():
+ *     return expr
+ */

noether.nimble

@@ -0,0 +1,14 @@
+# Package
+
+version       = "0.1.0"
+author        = "Emile Clark-Boman"
+description   = "Type theoretic imperative and logic language for mathematical programming"
+license       = "MIT"
+srcDir        = "src"
+installExt    = @["nim"]`
+bin           = @["noether"]
+
+
+# Dependencies
+
+requires "nim >= 2.2.0"

py/NOTES

@@ -6,3 +6,11 @@ NOTE: currently my "primitive roots" are actually just the numbers that generate
 
 This site is useful as a reference:
 	https://owlsmath.neocities.org/Primitive%20Root%20Calculator/calculator
+
+
+2. Make Noether into a mathematical programming language (like MATLAB), 
+	with the ability to create custom types (ie the integers modulo n)
+	with specific properties like operator overloading. Then you could
+	create functions that check whether a set and an operator form a
+	group or not, etc.
+	2.1 Use ^ to indicate exponentiation, and use ^| to indicate xor

py/m.py

@@ -0,0 +1,107 @@
+#!/usr/bin/env python3
+import sys
+import readline
+
+from noether.math import *
+from noether.cli import *
+
+
+PROMPT = '[n]: '
+
+'''
+Pairwise orbit cumulative summation (cum orb) 
+'''
+def orb_cum(cum, orb):
+    for i in range(len(cum)):
+        cum[i] += orb[i]
+
+def main():
+    while True:
+        n = None
+        strlen_n = None
+        try:
+            uprint(PROMPT, color=Color.Blue, end='')
+            n = input()
+            strlen_n = len(n)
+            n = int(n)
+        except ValueError:
+            continue
+
+        # calculate phi of n
+        phi = totient(n)
+        # determine if n is prime
+        prime = n - 1 == phi
+        if prime:
+            uprint('', moveup=1, end='', flush=False)
+            column = len(PROMPT) + strlen_n + 1
+            sys.stdout.write(f'\033[{column}C')
+            uprint('[PRIME]', color=Color.Magenta, style=Color.Bold, flush=True)
+        # primitive root values
+        proot_v = []
+        # primitive root count
+        proot_c = 0
+        # cumulative sum of primitive root orbits
+        prorb_cum = []
+        
+        # calculate left padding to align i values
+        # lpadded = strlen_n
+        # calculate right padding to align len(orb) values
+        rpadded = len(str(phi))
+    
+        # find all invertible elements (skipped for now)
+        for a in range(n):
+            orb, ord, periodic = orbit(a, n)
+
+            # check if `a` is a primitive root
+            # NOTE: this should actually be `proot = (ord == phi(n))`
+            # proot = (ord + 1 == n)
+            proot = (ord == phi)
+            proot_c += proot 
+
+            # calculate padding
+            lpad = ' ' * (strlen_n - len(str(a)))
+            rpad = ' ' * (rpadded - len(str(ord)))
+            # calculate coloring
+            color_a = Color.Red
+            color_ord = None
+            color_orb = None
+            style_ord = None
+            style_orb = None                
+            if proot:
+                color_a = Color.Green
+                color_ord = Color.Yellow
+                color_orb = Color.Green
+                style_ord = Color.Bold
+                style_orb = Color.Bold
+                proot_v.append(a)
+                if not prorb_cum:
+                    prorb_cum = orb
+                else:
+                    orb_cum(prorb_cum, orb)
+            elif gcd(a, n) == 1:
+                color_a = Color.Yellow
+            
+            uprint(f'{lpad}{a}', color=color_a, style=Color.Bold, end=' ', flush=False)
+            uprint('->', end=' ', flush=False)
+            uprint(f'{ord}{rpad}', color=color_ord, style=style_ord, end=' ', flush=False)
+            uprint('|', end=' ', flush=False)
+            uprint(f'{orb}', color=color_orb, style=style_orb, flush=True)
+        uprint('Cum Orb:   ', end='', color=Color.Cyan)
+        uprint(f'{prorb_cum}', flush=True)
+        prorb_cum_mod = [x % n for x in prorb_cum]
+        uprint(f'           {prorb_cum_mod}', flush=True)
+
+        uprint('Roots:     ', end='', color=Color.Cyan)
+        uprint(proot_v, flush=True)
+        root_delta = [proot_v[i+1] - proot_v[i] for i in range(proot_c - 1)]
+        uprint('Delta:     ', end='', color=Color.Cyan)
+        uprint(root_delta, flush=True)
+        
+        uprint('Roots/Phi: ', end='', color=Color.Cyan)
+        uprint(f'{proot_c}/{phi}\n', flush=True)
+
+if __name__ == '__main__':
+    try:
+        main()
+    except (KeyboardInterrupt, EOFError):
+        pass     

py/mquiet.py

@@ -1,6 +1,7 @@
 # Modulo Test
-from prbraid.math import *
-from prbraid.color import *
+from noether.lib.groups import *
+from noether.cli.ansi import *
+from noether.cli._old import *
 
 import sys
 
@@ -18,7 +19,7 @@ def main():
         n = None
         strlen_n = None
         try:
-            uprint(PROMPT, color=Color.Blue, end='')
+            uprint(PROMPT, color=Color.BLUE, end='')
             n = input()
             strlen_n = len(n)
             n = int(n)
@@ -43,7 +44,7 @@ def main():
   
         # find all invertible elements (skipped for now)
         for a in range(n):
-            orb, ord = orbit(a, n)
+            orb, ord, periodic = cyclic_subgrp(a, n)
             # check if `a` is a primitive root
             proot = (ord + 1 == n)
             proot_c += proot 

py/noether.py

@@ -1,105 +1,34 @@
-#!/usr/bin/env python3
-import sys
-import readline
+from noether.cli.style import *
+from noether.cli.prompt import *
+from noether.lib.structs import Result
+          
+class Noether(Prompt):
+    DEFAULT_PROMPT = style('~>> ', Color.BLUE)
+    def __init__(self) -> None:
+        super().__init__()
 
-from noether.math import *
-from noether.cli import *
+    def _parse(self, command: str) -> int:
+        try:
+            return Result.succeed(int(command))
+        except ValueError:
+            return Result.fail('Not an integer.')
 
-
-PROMPT = '[n]: '
-
-'''
-Pairwise orbit cumulative summation (cum orb) 
-'''
-def orb_cum(cum, orb):
-    for i in range(len(cum)):
-        cum[i] += orb[i]
+    def _exec(self, command: int) -> None:
+        print(style(f'OMG {command}', Color.CYAN))
 
 def main():
-    while True:
-        n = None
-        strlen_n = None
-        try:
-            uprint(PROMPT, color=Color.Blue, end='')
-            n = input()
-            strlen_n = len(n)
-            n = int(n)
-        except ValueError:
-            continue
+    try:
+        noether = Noether()
+        while True:
+            noether.prompt()
+    except (KeyboardInterrupt, EOFError):
+        err = style('Exit Requested...', Effect.ITALICS)
+        print('\n', style('[!]', Color.RED), err)
 
-        # calculate phi of n
-        phi = totient(n)
-        # determine if n is prime
-        prime = n - 1 == phi
-        if prime:
-            uprint('', moveup=1, end='', flush=False)
-            column = len(PROMPT) + strlen_n + 1
-            sys.stdout.write(f'\033[{column}C')
-            uprint('[PRIME]', color=Color.Magenta, style=Color.Bold, flush=True)
-        # primitive root values
-        proot_v = []
-        # primitive root count
-        proot_c = 0
-        # cumulative sum of primitive root orbits
-        prorb_cum = []
-        
-        # calculate left padding to align i values
-        # lpadded = strlen_n
-        # calculate right padding to align len(orb) values
-        rpadded = len(str(phi))
-    
-        # find all invertible elements (skipped for now)
-        for a in range(n):
-            orb, ord = orbit(a, n)
-
-            # check if `a` is a primitive root
-            proot = (ord + 1 == n)
-            proot_c += proot 
-
-            # calculate padding
-            lpad = ' ' * (strlen_n - len(str(a)))
-            rpad = ' ' * (rpadded - len(str(ord)))
-            # calculate coloring
-            color_a = Color.Red
-            color_ord = None
-            color_orb = None
-            style_ord = None
-            style_orb = None                
-            if proot:
-                color_a = Color.Green
-                color_ord = Color.Yellow
-                color_orb = Color.Green
-                style_ord = Color.Bold
-                style_orb = Color.Bold
-                proot_v.append(a)
-                if not prorb_cum:
-                    prorb_cum = orb
-                else:
-                    orb_cum(prorb_cum, orb)
-            elif gcd(a, n) == 1:
-                color_a = Color.Yellow
-            
-            uprint(f'{lpad}{a}', color=color_a, style=Color.Bold, end=' ', flush=False)
-            uprint('->', end=' ', flush=False)
-            uprint(f'{ord}{rpad}', color=color_ord, style=style_ord, end=' ', flush=False)
-            uprint('|', end=' ', flush=False)
-            uprint(f'{orb}', color=color_orb, style=style_orb, flush=True)
-        uprint('Cum Orb:   ', end='', color=Color.Cyan)
-        uprint(f'{prorb_cum}', flush=True)
-        prorb_cum_mod = [x % n for x in prorb_cum]
-        uprint(f'           {prorb_cum_mod}', flush=True)
-
-        uprint('Roots:     ', end='', color=Color.Cyan)
-        uprint(proot_v, flush=True)
-        root_delta = [proot_v[i+1] - proot_v[i] for i in range(proot_c - 1)]
-        uprint('Delta:     ', end='', color=Color.Cyan)
-        uprint(root_delta, flush=True)
-        
-        uprint('Roots/Phi: ', end='', color=Color.Cyan)
-        uprint(f'{proot_c}/{phi}\n', flush=True)
 
 if __name__ == '__main__':
     try:
         main()
     except (KeyboardInterrupt, EOFError):
-        pass     
+        # handles premature SIGINT/EOF
+        pass

py/noether/cli.py

@@ -1,59 +0,0 @@
-from enum import Enum
-from typing import Optional
-
-class Color(Enum):
-    Reset = 0
-    Bold = 1
-    Italics = 2  
-    Underline = 4 
-    
-    Black = 30
-    Red = 31
-    Green = 32
-    Yellow = 33
-    Blue = 34
-    Magenta = 35
-    Cyan = 36
-    White = 37
-
-    # escape sequence format string
-    __fescseq = '\033[{0}'
-    # ansi reset code
-    __ansi_rst = '\033[0m'
-    
-    @staticmethod
-    def _ansi_ret(ansi):
-        return ansi, Color.__ansi_white
-
-    @staticmethod
-    def code(color: 'Color'):
-        return Color.__fescseq.format(f'{color.value}m')
-
-    # move the cursor up n lines
-    @staticmethod
-    def mvup_code(n: int):
-        return Color.__fescseq.format(f'{n}A')
-    
-    def ansi(self):
-        code = Color.code(self)
-        if self == Color.White:
-            return code, ''
-        return code, Color.__ansi_rst
-
-# !! ULTRA PRINT !!
-def uprint(text: str, 
-           color: Optional[Color] = None,
-           style: Optional[Color] = None,
-           moveup: int = 0, 
-           end: str = '\n', 
-           flush: bool = True):
-    if color is not None:
-        c = color.ansi()
-        text = f'{c[0]}{text}{c[1]}'
-    if style is not None:
-        s = style.ansi()
-        tail = '' if (c is not None and c[1] == '') else s[1]
-        text = f'{s[0]}{text}{tail}'
-    if moveup > 0:
-        text = Color.mvup_code(moveup) + text
-    print(text, end=end, flush=flush)

py/noether/cli/prompt.py

@@ -0,0 +1,66 @@
+'''
+===== Prompt Handling =====
+This file implements the Prompt class, allowing for
+inheritance and instantiation of Prompt objects.
+The CLI class uses these instead of containing the 
+logic immediately within itself.
+'''
+
+from typing import Any
+
+from noether.cli.style import *
+from noether.lib.structs import Result
+
+class Prompt:
+    DEFAULT_PROMPT = 'DEF> '
+    def __init__(self) -> None:
+        self._prompt = self.DEFAULT_PROMPT
+
+    '''
+    Prompt and await command via stdin.
+    '''
+    def prompt(self):
+        command = self.__request()
+        result = self._parse(command)
+        if result.success:
+            self._exec(result.value)
+        else:
+            self.__parse_error(result)
+
+    '''
+    !! OVERRIDE ON INHERITANCE !!
+    Handles the parsing of a given command.
+    '''
+    def _parse(self, command: str) -> Result:
+        return Result.succeed(command)
+
+    def __parse_error(self, error: Result) -> None:
+        err = f'    ↳ {style(error.reason, Effect.ITALICS)}'
+        print(style(err, Effect.DIM))
+
+    '''
+    !! OVERRIDE ON INHERITANCE !!
+    Handles the execution of a command that
+    was successfully parsed by a Prompt inheritor.  
+    '''
+    def _exec(self, command: Any) -> None:
+        pass
+    
+    '''
+    Internal use only. Handles a raw request with no validation. 
+    '''
+    def __request(self) -> None:
+        print(self.__get_prompt(), end='', flush=True)
+        return input()
+
+    '''
+    !! OVERRIDE ON INHERITANCE !!  
+    '''
+    def _style_prompt(self, prompt: str) -> str:
+        return prompt
+
+    def __get_prompt(self) -> str:
+        return self._style_prompt(self._prompt)
+
+    def set_prompt(self, prompt: str) -> None:
+        self._prompt = prompt

py/noether/cli/style.py

@@ -8,8 +8,12 @@ for management of the CLI.
 from sys import stdout
 from enum import StrEnum
 
+# Removes ALL set colors/styling
 RESET = '\x1b[0m'
 
+'''
+Implements text foreground coloring. 
+'''
 class Color(StrEnum):
     BLACK   = '\x1b[30m'
     RED     = '\x1b[31m'
@@ -20,7 +24,18 @@ class Color(StrEnum):
     CYAN    = '\x1b[36m'
     WHITE   = '\x1b[37m'
 
-class Style(StrEnum):
+    '''
+    Handles the application of a Color to a given text.
+    Unset the `temp` flag to leave this style on (after the given text) 
+    '''
+    @staticmethod
+    def apply(color: 'Color', text: str, temp: bool = True) -> str:
+        return color + text + Color.WHITE if temp else ''
+
+'''
+Implements text effects.  
+'''
+class Effect(StrEnum):
     BOLD      = '\x1b[1m'
     DIM       = '\x1b[2m'
     ITALICS   = '\x1b[3m'
@@ -29,14 +44,39 @@ class Style(StrEnum):
     REVERSE   = '\x1b[7m'
     HIDE      = '\x1b[8m'
 
-    _DISABLE = [
-        '\x1b[21m', # BOLD
-        '\x1b[22m', # DIM
-        '\x1b[24m', # UNDERLINE
-        '\x1b[25m', # BLINK
-        '\x1b[27m', # REVERSE
-        '\x1b[28m'  # HIDE
-    ]
+    '''
+    Returns the opposite ESC code to a given Effect.
+    ie the opposite of BOLD '\x1b[1m]' is '\x1b[21m'
+    '''
+    @staticmethod
+    def _inverse(effect: 'Effect') -> str:
+        return f'{effect[:2]}2{effect[2:]}'
+
+    '''
+    Handles the application of a Effect to a given text.
+    Unset the `temp` flag to leave this style on (after the given text) 
+    '''
+    @staticmethod
+    def apply(effect: 'Effect', text: str, temp: bool = True) -> str:
+        return effect + text + Effect._inverse(effect) if temp else ''
+
+'''
+Applies styling (color/effects/etc) to a given string
+Unset the `temp` flag to leave this style on (after the given text) 
+'''
+def style(text: str, *args: Color | Effect, temp: bool = True) -> str:
+    # unsures we don't add redundant "set white" commands
+    unset_color = False
+    for arg in args:
+        unset = temp
+        if isinstance(arg, Color):
+            unset_color |= temp
+            unset = False
+        text = type(arg).apply(arg, text, temp=True)
+    if unset_color:
+        text += Color.WHITE
+    return text
+
 
 '''
 Implements cursor movement functionality.
@@ -48,8 +88,8 @@ NOTE:
 '''
 class Cursor(StrEnum):
     # SAVE current / RESTORE last saved cursor position
-    SAVE = f'\x1b[7'
-    RESTORE = f'\x1b[8'
+    _SAVE = f'\x1b[7'
+    _RESTORE = f'\x1b[8'
     
     _MV_UP     = 'A'
     _MV_DOWN   = 'B'
@@ -137,7 +177,7 @@ class Cursor(StrEnum):
     '''
     @staticmethod
     def save() -> None:
-        stdout.write(Cursor.SAVE)
+        stdout.write(Cursor._SAVE)
 
     '''
     Restores the cursor position to a saved position.
@@ -145,7 +185,7 @@ class Cursor(StrEnum):
     '''
     @staticmethod
     def restore() -> None:
-        stdout.write(Cursor.RESTORE)
+        stdout.write(Cursor._RESTORE)
 
 '''
 Handles erasing content displayed on the screen.
@@ -155,18 +195,40 @@ via these sequences. The \r code should be given after.
 class Erase(StrEnum):
     # erase everything from the current cursor
     # position to the START/END of the screen
-    ER_SCR_END    = '\x1b[0J'
-    ER_SCR_START  = '\x1b[1J'
-    # ER_SCR_ALL    = '\x1b[2J'
-    ER_SCR_ALL    = '\x1b[3J' # erase screen and delete all saved cursors
+    _SCR_AFTER  = '\x1b[0J'
+    _SCR_BEFORE = '\x1b[1J'
+    _SCR_ALL    = '\x1b[3J' # erase screen and delete all saved cursors
     
-    # ER_SAVED      = '\x1b[3J' # erase saved lines
-
     # erase everything from the current cursor
     # position to the START/END of the current line
-    ER_LINE_END   = '\x1b[0K'
-    ER_LINE_START = '\x1b[1K'
-    ER_LINE_ALL   = '\x1b[2K'
+    _LINE_AFTER  = '\x1b[0K'
+    _LINE_BEFORE = '\x1b[1K'
+    _LINE_ALL    = '\x1b[2K'
 
+    '''
+    Erase characters on the entire screen.
+    Set `before` flag to only erase before the cursor,
+    set `after` flag to only erase after the cursor.
+    '''
     @staticmethod
-    # TODO COME BACK HERE
+    def screen(before: bool = False, after: bool = False) -> None:
+        if before:
+            stdout.write(Erase._SCR_BEFORE)
+        elif after:
+            stdout.write(Erase._SCR_AFTER)
+        else:
+            stdout.write(Erase._SCR_ALL)
+
+    '''
+    Erase characters on the current line.
+    Set `before` flag to only erase before the cursor,
+    set `after` flag to only erase after the cursor.
+    '''
+    @staticmethod
+    def line(before: bool = False, after: bool = False) -> None:
+        if before:
+            stdout.write(Erase._LINE_BEFORE)
+        elif after:
+            stdout.write(Erase._LINE_AFTER)
+        else:
+            stdout.write(Erase._LINE_ALL)

py/noether/cmd/cycsub.py

@@ -0,0 +1,60 @@
+from sys import stdout
+
+from noether.cli.style import *
+from noether.cli.prompt import *
+from noether.lib.structs import Result
+
+from noether.lib.util import digits
+from noether.lib.groups import cyclic_subgrp
+from noether.lib.primes import totient, is_prime
+
+class cycsub(Prompt):
+    DEFAULT_PROMPT = style('[n]: ', Color.BLUE)
+    def __init__(self, ignore_zero: bool = True) -> None:
+        super().__init__()
+        self.ignore_zero = ignore_zero
+    
+    def _parse(self, command: str) -> int:
+        try:
+            return Result.succeed(int(command))
+        except ValueError:
+            return Result.fail('Not an integer.')
+
+    def _exec(self, n: int) -> None:
+        phi = totient(n)
+        lpadding = digits(n)
+        rpadding = digits(phi)
+        if is_prime(n, phi=n):
+            Cursor.save()
+            Cursor.move_y(-1, reset=False)
+            Cursor.set_x(len(self.DEFAULT_PROMPT) + lpadding + 1)
+            stdout.write(style('[PRIME]', Color.MAGENTA, Effect.BOLD))
+            Cursor.restore()
+            stdout.flush()
+
+        # keeps track of all primitive roots
+        # (note that there will be exactly totient(phi) of them)
+        proots = []
+        for g in range(n):
+            G, order, periodic = cyclic_subgrp(g, n, ignore_zero=self.ignore_zero)
+            primitive = (order == phi) # primitive root
+
+            lpad = ' ' * (lpadding - digits(a))
+            rpad = ' ' * (rpadding - digits(order))
+
+            color_g = Color.RED
+            style_G = []
+            style_order = []
+            if primitive:
+                color_g = Color.GREEN
+                style_G = [Color.GREEN, Effect.BOLD]
+                style_order = [Color.YELLOW, Effect.BOLD]
+                proots.append(g)
+            elif gcd(g, n) == 1:
+                color_g = Color.Yellow
+            line = style(f'{lpad}{g}', color_g, Effect.BOLD) + \
+                   '-> ' + \
+                   style(f'{order}{rpad} ', *style_order) + \
+                   '| ' + \
+                   style(str(G), *style_G)
+            print(line, flush=True)

py/noether/exceptions.py

@@ -0,0 +1,3 @@
+class PromptParseError(Exception):
+    def __init__(self, message: str) -> None:
+        super().__init__(message)

py/noether/lib/groups.py

@@ -0,0 +1,37 @@
+'''
+This library exists to isolate all math functions
+related to groups and their representations. 
+'''
+
+from math import gcd
+
+'''
+Returns the multiplicative cyclic subgroup 
+generated by an element g modulo m.
+Returns the cyclic subgroup as a list[int],
+    the order of that subgroup, and a boolean
+    indicating whether g is infinitely repeating
+    with period == ord<g> (or otherwise if it
+    terminates with g**ord<g> == 0).
+'''
+def cyclic_subgrp(g: int, 
+                  m: int, 
+                  ignore_zero: bool = True) -> tuple[list[int], int, bool]:
+    G = []
+    order = 0
+    periodic = True
+    a = 1 # start at identity
+    for _ in range(m):
+        a = (a * g) % m
+        if a == 0:
+            if not ignore_zero:
+                G.append(a)
+                order += 1
+            periodic = False
+            break
+        # check if we've reached something periodic
+        elif a in G[:1]:
+            break        
+        G.append(a)
+        order += 1
+    return G, order, periodic

py/noether/lib/primes.py

@@ -0,0 +1,36 @@
+from math import gcd
+
+'''
+Euler's Totient (Phi) Function
+'''
+def totient(n):
+    phi = int(n > 1 and n)
+    for p in range(2, int(n ** .5) + 1):
+        if not n % p:
+            phi -= phi // p
+            while not n % p:
+                n //= p
+    #if n is > 1 it means it is prime
+    if n > 1: phi -= phi // n 
+    return phi
+
+'''
+Tests the primality of an integer using its totient.
+NOTE: If totient(n) has already been calculated 
+      then pass it as the optional phi parameter. 
+'''
+def is_prime(n: int, phi: int = None):
+    return n - 1 == phi if phi is not None else totient(n):
+
+'''
+Prime number generator function.
+Returns the tuple (p, phi(p)) where p is prime
+    and phi is Euler's totient function.
+'''
+def prime_gen():
+    n = 1
+    while True:
+        n += 1
+        phi = totient(n)
+        if is_prime(n, phi=phi):
+            return n, phi

py/noether/lib/structs/__init__.py

@@ -0,0 +1 @@
+from noether.lib.structs.__result import Result

py/noether/lib/structs/__result.py

@@ -0,0 +1,19 @@
+from enum import Enum
+from typing import Optional
+
+class Result:
+    def __init__(self, 
+                 success: bool, 
+                 reason: str, 
+                 value: Optional[any] = None) -> None:
+        self.success = success
+        self.reason = reason
+        self.value = value
+
+    @classmethod
+    def succeed(cls, value: any, reason: str = 'Ok') -> 'Result':
+        return cls(True, reason, value=value)
+
+    @classmethod
+    def fail(cls, reason: str, value: Optional[any] = None) -> 'Result':
+        return cls(False, reason, value=value)

py/noether/lib/util.py

@@ -0,0 +1,2 @@
+def digits(n: int) -> int:
+    return len(str(n))

py/noether/math.py

@@ -1,42 +0,0 @@
-from math import gcd
-
-# Euler's Totient (Phi) Function
-def totient(n):
-    phi = int(n > 1 and n)
-    for p in range(2, int(n ** .5) + 1):
-        if not n % p:
-            phi -= phi // p
-            while not n % p:
-                n //= p
-    #if n is > 1 it means it is prime
-    if n > 1: phi -= phi // n 
-    return phi
-
-def is_prime(n):
-    return n - 1 == totient(n)
-
-def orbit(b, m):
-    orb = []
-    ord = 0
-    x = 1 # start at identity
-    for i in range(m):
-        x = (x * b) % m
-        if x in orb:
-            break        
-        orb.append(x)
-        ord += 1
-    return orb, ord
-
-def order(b, m):
-    return len(orbit(b, m))
-
-
-'''
-Functions for Testing my Conjectures 
-
-The conjecture is specifically that, for all positive integers n
-where n + 1 is prime, then conj_phigcd(n) is also prime.
-'''
-def conj_phigcd(n):
-    phi = totient(n)
-    return phi / gcd(n, phi) - 1

py/primes.py

@@ -1,80 +0,0 @@
-# Modulo Test
-from prbraid.math import *
-from prbraid.color import *
-
-import sys
-from math import gcd
-from time import sleep
-
-PROMPT = '[n]: '
-
-'''
-Modify the body of this function, it will be run
-against every prime number ascending.
-'''
-def test_function(p: int, phi: int):
-    p_color = Color.Green
-    result_color = Color.Yellow
-    
-    result = phi / gcd(p, phi) - 1
-    if result < 0 or not is_prime(result):
-        p_color = Color.Red
-        result_color = Color.Red
-    uprint(p, color=p_color, style=Color.Bold, end=' -> ', flush=False)
-    uprint(result, color=result_color, flush=True)
-    sleep(0.1)
-    
-
-def main():
-    n = -1
-    while True:
-        n += 1
-
-        # calculate phi of n
-        phi = totient(n)
-        # determine if n is prime
-        prime = n - 1 == phi
-        if not prime:
-            continue
-        
-        # # primitive root values
-        # proot_v = []
-        # # primitive root count
-        # proot_c = 0
-        # # cumulative sum of primitive root orbits
-        # prorb_cum = []       
-  
-        # # find all invertible elements (skipped for now)
-        # for a in range(n):
-        #     orb, ord = orbit(a, n)
-        #     # check if `a` is a primitive root
-        #     proot = (ord + 1 == n)
-        #     proot_c += proot 
-
-        #     if proot:
-        #         proot_v.append(a)
-        #         if not prorb_cum:
-        #             prorb_cum = orb
-        #         else:
-        #             orb_cum(prorb_cum, orb)
-        #         print(a)            
-        # uprint('Cum Orb:   ', end='', color=Color.Cyan)
-        # uprint(f'{prorb_cum}', flush=True)
-        # prorb_cum_mod = [x % n for x in prorb_cum]
-        # uprint(f'           {prorb_cum_mod}', flush=True)
-
-        # uprint('Roots:     ', end='', color=Color.Cyan)
-        # uprint(proot_v, flush=True)
-        # root_delta = [proot_v[i+1] - proot_v[i] for i in range(proot_c - 1)]
-        # uprint('Delta:     ', end='', color=Color.Cyan)
-        # uprint(root_delta, flush=True)
-        
-        # uprint('Roots/Phi: ', end='', color=Color.Cyan)
-        # uprint(f'{proot_c}/{phi}\n', flush=True)
-        test_function(n, phi)
-
-if __name__ == '__main__':
-    try:
-        main()
-    except (KeyboardInterrupt, EOFError):
-        pass     

src/noether.nim

@@ -0,0 +1,7 @@
+# This is just an example to get you started. A typical hybrid package
+# uses this file as the main entry point of the application.
+
+import noether/submodule
+
+when isMainModule:
+  echo(getWelcomeMessage())

src/noether/lexer.nim

@@ -0,0 +1,29 @@
+import std/streams
+
+type
+  nlLexer* = object
+    stream: Stream
+    pos: Natural
+
+proc newLexerFromStream(stream: Stream): nlLexer =
+  result = nlLexer(
+    stream: stream,
+    pos: 0,
+  )
+)
+
+proc newLexer*(content: string, isFile: bool): nlLexer =
+  result = newLexerFromStream(
+    streamFile(content) if isFile else streamString(content)
+  )
+)
+
+proc streamFile(filename: string): FileStream =
+  result = newFileStream(filename, fmRead)
+
+proc streamString(str: string): StringStream =
+  result = newStringStream(str)
+
+
+proc nextToken*(lexer: nlLexer): nlToken =
+  result = newToken[]

src/noether/submodule.nim

@@ -0,0 +1,6 @@
+# This is just an example to get you started. Users of your hybrid library will
+# import this file by writing ``import srcpkg/submodule``. Feel free to rename or
+# remove this file altogether. You may create additional modules alongside
+# this file as required.
+
+proc getWelcomeMessage*(): string = "Hello, World!"

tests/config.nims

@@ -0,0 +1 @@
+switch("path", "$projectDir/../src")

tests/test1.nim

@@ -0,0 +1,12 @@
+# This is just an example to get you started. You may wish to put all of your
+# tests into a single file, or separate them into multiple `test1`, `test2`
+# etc. files (better names are recommended, just make sure the name starts with
+# the letter 't').
+#
+# To run these tests, simply execute `nimble test`.
+
+import unittest
+
+import src/submodule
+test "correct welcome":
+  check getWelcomeMessage() == "Hello, World!"