How to Solve a Symbolic System of Linear Equations in CalcPad?

[Mykola-special]

Hello! I recently started exploring CalcPad for my structural engineering classes, and I’ve found it very helpful and easy to use. Big kudos to the team for developing this tool!

I have a question: how can I solve a system of linear equations in CalcPad? For example, something similar to solving equations using the SymPy library in Python. Or is there an example available? I couldn’t find any in the Examples repository.

Thank you for the answer

#################################
from sympy import symbols, Eq, solve

### Define the variables
a, v = symbols('a v')


### Define the equations
eq1 = Eq(a*(11 - v), 34.93)
eq2 = Eq((a + 6.25) *  v, 34.93)

### Solve the system of equations
solution = solve((eq1, eq2), (a, v))

### Output the solution
for i in solution:
    if i[0] > 0 and i[1] > 0:
        print(i)

[Proektsoftbg]

Hi!

Calcpad does not include symbolic engine and will probably never will. It is mostly aimed to automate the development of (structural) engineering calculation notes. So, it includes only numerical calculations. It can solve systems of linear equations of type Ax = b, where A is a matrix with equation coefficients, b is the right-hand side vector and x is the unknown vector. Examples are provided here:
https://github.com/Proektsoftbg/Calcpad/blob/main/Examples/Mathematics/Matrices/Matrix%20math%20functions.cpd

However, what you have in your example are not actually linear equations. When you expand the brackets, you will end up with a*v which is a quadratic term, so this is a system of nonlinear equations. You can also solve it numerically with Calcpad. Although there is not a native function for that, you can write your own solution with just a few lines of code using some of the commonly available methods:

1. Fixed point iteration method
2. Newton-Raphson's method
3. Broyden’s method, etc.

An example how to do that for a system of four equations is provided in this worksheet:

https://github.com/Proektsoftbg/Calcpad/blob/main/Examples/Mathematics/System%20of%20nonlinear%20equations.cpd

Please note that the symbolic way is suitable only for small systems with less equations. Otherwise, the formulas for the calculation of the separate unknowns become too long and complex. Sometimes they cannot be even delivered, if some of the equations are transcendental.

[Mykola-special]

Thank you for your response! Even with such a simple problem, I know I will learn a great deal.