Introduction

SimulaMath module is built on top of the scientific Python packages like Numpy, Scipy, Sympy, and Mpmath.

Special Simula Syntax

  • Fractions: on simula, the result of the division of two Integers is a fraction. But on Python, it is a float number.

    simula : 2/3
2/3
simula : 4/10
2/5
simula : 1/2 + 1/5 + 3/5
13/10
simula : int(1)/int(2)
0.5

  • Multiplication: the multiplication under simula is “*” as in Python.

    simula : x = 2; x
2
simula : 3*x
6

    There are some special cases of multiplication.

    When a number is followed by a variable, it means multiplication.

    simula : x = 2; x
2
simula : 3x
6
simula : 5x -2
8

    When a number is followed by an open parenthesis “(”, it means multiplication.

    simula : x = 2; x
2
simula : 3(x+2)
12
simula : 5(2x-1)
15

    When a closed parenthesis “)” is followed by an open parenthesis “(”, it means multiplication.

    simula : x = 3; x
3
simula : (x-1)(x+2)
10
simula : 5(2x-1)(x-1)
50

  • Power: the power under simula is “^” or “**” as in Python.

    simula : 2^3
8
simula : x = 3; 2x^2
18
simula : (x - 1)(2x^3 -10)
88

    Remark : The symbol “^” means bitwise XOR in Python, but on simula, the equivalent operator is “^^”.

    EXAMPLE:

    simula : bin(0b100101 ^^ 0b001010)
'0b101111'

  • Factorial : A number followed by “!” symbol means factorial.

    simula : 3!
6
simula : 3! == 6
True
simula : 3! != 6
False
simula : 6!/4!
30

  • Special Sequences : [a, b, …, n], (a, b, …, n) or {a, b, …, n}.

    simula : [1, 3, ..., 11]
[1, 3, 5, 7, 9, 11]
simula : {1, 3, ..., 11}
{1, 3, 5, 7, 9, 11}
simula : (1, 3, ..., 11)
(1, 3, 5, 7, 9, 11)
simula : [10, 20, ..., 100]
[10, 20, 30, 40, 50, 60, 70, 80, 90, 100]

  • Symbolic variables:

Symbolic Variables

simula.symbols.var(names, domain=None, parity=None, *, globals=True, **kwargs)

Create symbols and inject them into the global namespace.

Valid kwargs:

  • commutative : True or False

EXAMPLES:

simula : var('x')
x
simula : x
x
simula : var('x, y', "RR")  # x and y are real numbers
(x, y)
simula : x.is_real and y.is_real
True
simula : var('z', "RR*+")  # z is a positive real number
z
simula : z > 0
True
simula : z < 0
False
simula: z > 4
z > 4
simula : n = var('n', "NN"); n  # n is a non-negative integer number
n
simula : n >= 0
True

simula : var('x, y2, ab')
(x, y2, ab)
simula : y2
y2
simula : var(('a', 'b', 'c'))
(a, b, c)
simula : var(['a', 'b', 'c'])
[a, b, c]
simula : var({'a', 'b', 'c'})
{a, b, c}
simula : var('x:z')
(x, y, z)
simula : var('x1:4')
(x1, x2, x3)
simula : xa, yb = var('x((a:b))')
simula : xa
x(a)
Parameters

globals (bool) –

  • Functions : You can define a function easily on simula like in mathematics.

    simula : x = var('x')
simula : f(x) = x^2-2x-2; f
Function defined by x |--> x^2 - 2x - 2
simula : f(2)
-2
simula : f(2x-1)
-4x + (2x - 1)^2
simula : y = var('y')
simula : g(x, y) = x - y + 1; g
Function defined by (x, y) |--> x - y + 1
simula : g(x, x)
1

  • Complex numbers: The imaginary unit is represented by I.

    simula : 3-5I
3-5I
simula : conjugate(3-5I)
3 + 5I
simula : real_part(3-5I)
3
simula : im_part(3-5I)
-5

    Python complex numbers are compatible with Simula complex numbers.

    simula : 2-5j
3-5I
simula : real_part(2-5j)
3

  • Polynomial ring : You can define a polynomial ring like in Sage.

    simula : R.<x, y, z> = QQ[]
simula : R
Multivariate Polynomial Ring in x, y, z over QQ with deglex order
simula : (x^2-1).factor()
(x - 1)*(x + 1)
simula : F.<w> = GF(3)[]; F
Univariate Polynomial Ring in w over GF(3) with deglex order
simula : 5w^4+10w^2-2
2w^4 + w^2 - 2

  • Finite Fields : You can define a finite field like in Sage.

    simula : G.<a> = GF(9); G
Finite Field of 9 elements defined by the quotient of F_3[a] by the ideal <a^2 + 2a + 2>
simula : a^2
a + 1
simula : 7a^3
2a + 1
simula : 1/a
a + 2

  • Binary, Octal and Hexadecimal:

    • Python Binary, Octal and Hexadecimal :

    simula : 0b1110
14
simula : bin(14)
'0b1110'
simula : oct(100)
'0o144'
simula : hex(1000)
'0x3e8'

    • Simula Binary, Octal and Hexadecimal :

    simula : Bin(14)
0b1110
simula : A = Bin(111); A
0b1101111
simula : A.to_list()
[1, 1, 0, 1, 1, 1, 1]
simula : A.to_list(10)
[0, 0, 0, 1, 1, 0, 1, 1, 1, 1]
simula : Bin(14) + Bin(17)
0b11111
simula : Bin(14) + Bin(17) == Bin(31)
True
simula : Bin(bin(14))
0b1110
simula : Oct(1000)
0o1750
simula : Hex(1000)
0x3e8
simula : Hex(100) + Hex(120) == Hex(220)
True

Simula Syntaxe as Python

Since SimulaMath language is based on Python, 99% of Python valid code work also on SimulaMath.

  • Float numbers:

    simula : 7.8
7.8
simula : 6.
6.0
simula : .5
0.5

  • Exponents:

    simula : 2e3
2000.0
simula : 3e-4
0.0003
simula : 3e+4
30000.0

  • Lists:

    simula : seq = [1,2,3,4,5]; print(seq)
[1, 2, 3, 4, 5]
simula : seq[0]
1
simula : seq[:2]
[1, 2]
simula : seq[-2:]
[4, 5]

    Comprehension of list

    simula : [i^2 for i in range(10)]
[0, 1, 4, 9, 16, 25, 36, 49, 64, 81]
simula : x = var('x'); f(x) = x^2-4x-1
simula : [f(i) for i in range(15)]
[-1, -4, -5, -4, -1, 4, 11, 20, 31, 44, 59, 76, 95, 116, 139]

  • Tuples:

    simula : seq2 = (1,2,3,4,5); print(seq2)
(1, 2, 3, 4, 5)
simula : seq[-1]
5
simula : seq[:2]
[1, 2]
simula : seq[-2:]
[4, 5]

  • Sets:

    simula : A = {1,2,3,4,5, 10, 15}; print(A)
{1, 2, 3, 4, 5, 10, 15}
simula : len(A)
7
simula : B = {-2, 4}; B
{4, -2}
simula : A | B
{1, 2, 3, 4, 5, 10, 15, -2}
simula : A & B
{4}

    Comprehension of Set

    simula : {i^2 for i in range(10)}
{0, 1, 64, 4, 36, 9, 16, 49, 81, 25}
simula : x = var('x'); f(x) = x^2-4x-1
simula : {f(i) for i in range(15)}
{4, 59, 11, 44, 76, 139, 20, 116, 95, -5, -4, -1, 31}

  • Strings:

    simula : word = "SimulaMath"; word
'SimulaMath'
simula : word.upper()
'SIMULAMATH'
simula : word.isalpha()
True
simula : word[2:]
'mulaMath'
simula : "Simula" "Math"
'SimulaMath'
simula : a, b = 2, 8
simula : "We get a = {} and b = {}".format(a, b)
'We get a = 2 and b = 8'
simula : f"We get a = {a} and b = {b}"
'We get a = 2 and b = 8'
simula : f"We get a = {2a} and b = {b^2}"
'We get a = 4 and b = 64'

  • Dictionaries:

    simula : dico = {'A': 0, "B": 1, 3: (1,2,3)}; print(dico)
{'A': 0, 'B': 1, 3: (1, 2, 3)}
simula : list(dico.keys())
['A', 'B', 3]
simula : list(dico.values())
[0, 1, (1, 2, 3)]
simula : del dico['A']; dico
{'B': 1, 3: (1, 2, 3)}
simula : dico["S"] = "SimulaMath"; dico
{'B': 1, 3: (1, 2, 3), 'S': 'SimulaMath'}

    Comprehension of Dictionary

    simula : {i : i^2 for i in range(10)}
{0: 0, 1: 1, 2: 4, 3: 9, 4: 16, 5: 25, 6: 36, 7: 49, 8: 64, 9: 81}
simula : x = var('x'); g(x) = 3x-1
simula : {2m: g(m) for m in range(15)}
{0: -1, 2: 2, 4: 5, 6: 8, 8: 11, 10: 14}

Note that conditions, loops (for loop, while loop) and functions syntax on SimulaMath and Python are the same.

  • Conditions

    simula : N = 194
simula : if N % 7 == 0:
. . . . . . :    print(f"{N} is a multiple of 7")
. . . . . . : else:
. . . . . . :     print(f"{N} is not a multiple of 7")
. . . . . . :
194 is not a multiple of 7
  • Loops
    simula : for i in range(9):
. . . . . . :    print(2i)
0
2
4
6
8
10
12
14
16
simula : for elt in [0, 5, ..., 30]:
. . . . . . :    print(elt)
0
5
10
15
20
25
30
  • Functions
    simula : def mean(L):
. . . . . . :    return sum(L)/len(L)
. . . . . . :
simula : mean([1,2,3,4,5])
3
simula : mean([3,4])
7/2

For more details on Python syntax, see the Python Doc

SimulaMath Editor

SimulaMath has a basic editor which allow you to save and load files with extension .sim and .py.

../_images/editor.PNG