sympy mathcad

Motivation

Inspired by https://github.com/mkhan45/CalcuLaTeX.

Wanted something that solved equations as well.

Based on sympy. Utilizes sympy’s solve function. Supports sympy syntax like units, pi, integrals and so on. Works well enough. Software is in “get something working” state. Good enough for my purpose.

Look at tips before using.

has both repl and input file version.

Usage

./sympy_mathcad.py

• opens repl

./sympy_mathcad.py input-file

• read and evaluate input-file

./sympy_mathcad.py term <<

• read from stdin and evaluate. input through here-doc.

Tips

• Press Enter to enter equations in mathcad like format. can be used to enter multi line equations. This is useful for keeping history intact.
• Press Alt-Enter or C-r to evaluate equations. Needs to be preceded by an Enter.
• Press C-f to flush or clear currently entered equations.
• Press C-s to show or print currently entered equations.
• Press C-c or C-q or C-d to quit.

text based

• Enter any substring of “evaluate” to evaluate equations.
• Enter any substring of “clear” to clear currently entered equations.
• Enter any substring of “print” to see currently entered equations.
• Enter any substring of “quit” to quit.

Examples

run in REPL

simple example

y = 3 * x
y = 10
x = ?

RESULTS

[x]
[{y: 10, x: 10/3}]
[{x: y/3}]
x  =  3.333

define and use units

in REPL ./sympy_mathcad.py

letter = Quantity("letter");
word = Quantity("word");
word.set_global_relative_scale_factor(5,letter);

gpt_size = 45e12*bit
file_size = 304e5*bit
file_words = 48902*word
gpt_words / gpt_size = file_words / file_size
gpt_words = ?
gpt_words = ? letter
e

Result

[{file_size: 30400000.0*bit, file_words: 48902.0*word, gpt_size: 45000000000000.0*bit, gpt_words: 72387828947.3684*word}]
[{gpt_words: file_words*gpt_size/file_size}]
gpt_words  =  7.239e+10*word
gpt_words  =  3.619e+11*letter

Numerical

caveats

• each variable needs to be defined with ?.
• need to a guess for value after “~” after “?”.

lasting_component = b * x * 1.30 ^ ( x / 12 )
temp_component = n * x * 1.30 ^ ( x / 12 )
130000 = temp_component
650000 - 130000 = lasting_component + (10400 - 6871 + 1105) * ( last - x ) * 1.30 ^ (( last - x ) / 12)
n + b = 1105
last = 100
n = ? ~ 100
b = ? ~ 100
last = ? ~ 144
lasting_component = ? ~ 100000
temp_component = ? ~ 130000
x = ? ~ 60

Result

-trying numerical solve--
[{n: 493.329807256738, b: 611.670192743262, last: 100.000000000000, lasting_component: 161184.513659930, temp_component: 130000.000000000, x: 64.4261206872098}]
n  =  493.3
b  =  611.7
last  =  100.0
lasting_component  =  1.612e+5
temp_component  =  1.300e+5
x  =  64.43

inequalities

caveats

• doesn’t work with multiple variable equations
• returns an Eq object
• doesn’t use units

x > 0
3423 = x ^ 4
x = ? mile

Result

Eq(x, 3423^(1/4))
Eq(x, 3423^(1/4))
x  =  Eq(x, 3423^(1/4))

Integrals

pu = integrate( 3 * x, x ) + x *newton
x = 20*newton
pu = ?

Result

{pu: 620*newton**2, x: 20*newton}]
[{pu: newton*x + 3*x**2/2}]
pu  =  620.0*newton**2

Integrals(2)

pu *newton = integrate( 3/newton * x, x ) + x
x = ?

Result

[{pu: x*(2*newton + 3*x)/(2*newton**2)}]
[{x: newton*(-sqrt(6*pu + 1)/3 - 1/3)}, {x: newton*(sqrt(6*pu + 1)/3 - 1/3)}]
x  =  newton*(-0.8165*(pu + 0.1667)**0.5 - 0.3333)

Diff eq

f = Function('f');
Derivative(f(x), x, x) + 9*f(x) = 0
f(x) = ?

Result

[Eq(9*f(x) + Derivative(f(x), (x, 2)), 0)]
[{f(x): C1*sin(3*x)/3 + C2*cos(3*x)/3}]
f(x)  =  0.3333*C1*sin(3*x) + 0.3333*C2*cos(3*x)