Workflow to convert formula (image) to python

motivation

Even if you find a mathematical formula in a dissertation or textbook, it takes time to utilize it. Even more, it takes more time to drop it in the document. Therefore, we created a workflow that can be used for programming and subsequent documentation by using mathematical expression images as input.

• Fully automatic is difficult, so it is a collaborative work with people.

Latex from image

Use a service called Mathpix to latex it. Registration is required, but it will latex the image with a nice touch.

It is like this

Get AsciiMath string

We will process the AsciiMath string and convert it to a form that can be used in python.

--Copy Ascii Math on the "data" tab of Mathpix Based on this character string, we will make it available in the program.

Preprocessing

Preprocess the string

--a: Paste the Ascii Math string --shoki_dict: The dictionary to be replaced first * Updated from time to time

translate_1.py

import re
# a = "sigma=(E alpha DeltaT)/(1-nu)*(1)/(1.5+3.25//beta-0.5 exp(-16//beta))"
# a = "M_(max)=(w*l^(2))/(8)"
a= "delta_(max)=(5*w*l^(4))/(384 E*I)"
# a ="K=(1.7 xx10^(5))/((delta_(1)+delta_(0))/(lambda_(1))+(delta_(2)+delta_(0))/(lambda_(2)))xx(0.6P)/(H)+(10^(6)lambda_(f))/(delta_(1)+delta_(2))"
shoki_tikan_dict = {" ":"*",
                   "xx":"*",
                   "^":"**",
                   "//":"/"}
for i in shoki_tikan_dict:
    a = a.replace(i,shoki_tikan_dict[i])
    
temp = re.sub("_\((.*?)\)","0",a)#So that you can get the variable ignoring the subscript_()To 0
hensu = re.findall("[A-Za-z]+",temp)#Extract variables
li_moji = list(set(hensu))#Clear variable duplication
print(a)
print(li_moji)

When the above is executed, the following is output. If there is something wrong with the formula here, correct it. Also, make sure that the variables are extracted properly. (Ignore the extra ones, OK. In the example, ignore "exp") sigma=(EalphaDeltaT)/(1-nu)(1)/(1.5+3.25/beta-0.5exp(-16/beta)) ['nu', 'sigma', 'DeltaT', 'beta', 'alpha', 'exp', 'E']

Convert expression

Convert Greek letters and subscripts into formulas

--moji_dict: List used when extracting parameters (Greek letters) * Updated from time to time

translate_2.py

moji_dict = {'lambda':"λ",
             'delta':"δ",
            'sigma':"σ",
            'alpha':"α",
            'DeltaT':"ΔT",
            'nu':'ν',
            'beta':'β',
            'epsi':"ε",
            'pi':'π',
            'mu':'μ'}


def tikan(moji_retsu,taisho,moji_dict):
#     print(taisho)
    taisho_temp = taisho+"_"
    seiki_1 = taisho_temp + "\(.*?\)"
    seiki_2 = taisho_temp + "\((.*?)\)"
    b = re.findall(seiki_1,moji_retsu)

    if len(b) != 0:
        if taisho in moji_dict:
            tikan_moji = moji_dict[taisho]
        else:
            tikan_moji = taisho
#             print(tikan_moji)
            
        newList = [re.sub(seiki_2,tikan_moji+"\\1",item) for item in b]
        moji_retsu = re.sub(seiki_2,tikan_moji+"\\1",moji_retsu)

    elif taisho in moji_dict:
        tikan_moji = moji_dict[taisho]
        newList = [tikan_moji]
        moji_retsu = moji_retsu.replace(taisho,tikan_moji)

    else:
        tikan_moji = taisho
        newList = [taisho]
        
    return moji_retsu,newList

li=[]
for i in li_moji:
    a,p = tikan(a,i,moji_dict)
    li.extend(p)
li=list(set(li))
li.sort()

a = re.sub("\(([0-9])\)","\\1",a)
print(a)
print(li)

When you execute the above, the following will be output σ=(EαΔT)/(1-ν)1/(1.5+3.25/β-0.5exp(-16/β)) ['E', 'exp', 'ΔT', 'α', 'β', 'ν', 'σ']

Next, add subscripts to form the formula. That's all you can do automatically, and the rest is manually made into an expression that can be used in python.

result_Eq.py

import math
σ=(E*α*ΔT)/(1-ν)*1/(1.5+3.25/β-0.5*math.exp(-16/β))

Now that the expression is complete, it's time to extract the parameters.

paramater_print.py

print("paramater_dict= {")
for i in li:
    print("    " + "'" + i +"':['',''],")
print("    }")

When you execute the above, the following will be output.

out.py

paramater_dict= {
    'E':['',''],
    'exp':['',''],
    'ΔT':['',''],
    'α':['',''],
    'β':['',''],
    'ν':['',''],
    'σ':['',''],
    }

This is the end of automatic operation, and the following actions are manually performed for the parameters.

--Delete unnecessary parameters --Change the order --Added description and units

result.py

paramater_dict= {
    'E':['Young's modulus','MPa'],
    'ΔT':['Inside and outside temperature difference','K'],
    'α':['Coefficient of linear expansion','/K'],
    'β':['Biot number',''],
    'ν':['Poisson's ratio',''],
    'σ':['Thermal stress','MPa'],
    }

It's a good idea, so can you use it?

run.py

import math

E = 200
ΔT = 10
α = 0.00005
β = 2
ν = 0.3

σ=(E*α*ΔT)/(1-ν)*1/(1.5+3.25/β-0.5*math.exp(-16/β))
print(σ)

If you do the above, you will get the answer. 0.045716739515498046

Documentation

At this point, you can easily document using sympy by applying the following article. Create mechanical design calculation material with python + sympy

Regarding the created formula

Create formulas as appropriate and share them below (updated as appropriate) Formulas and functions (updated as appropriate)

Afterword

I thought about using a library such as latex2sympy, but it was quite difficult. I learned regular expressions that I'm not good at! Mathpix cannot be used due to company security. .. .. I'm sorry