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Tutorial Release 10.4 The Sage Development Team https://doc.sagemath.org/pdf/en/tutorial/sage_tutorial.pdf

Sage is free, open-source math software that supports research and teaching in algebra, geometry, number theory, cryptography, numerical computation, and related areas. Both the Sage development model and the technology in Sage itself are distinguished by an extremely strong emphasis on openness, community, cooperation, and collaboration: we are building the car, not reinventing the wheel. The overall goal of Sage is to create a viable, free, open-source alternative to Maple, Mathematica, Magma, and MATLAB.

This tutorial is the best way to become familiar with Sage in only a few hours. You can read it in HTML or PDF versions, or from the Sage notebook (click Help, then click Tutorial to interactively work through the tutorial from within Sage).

This work is licensed under a Creative Commons Attribution-Share Alike 3.0 License.

https://creativecommons.org/licenses/by-sa/3.0/

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Kernel: SageMath 10.4

Solving Equations Exactly

The solve function solves equations. To use it, first specify some variables; then the arguments to solve are an equation (or a system of equations), together with the variables for which to solve:

from sage.all import *
x = var('x')
solve(x**2 + 3*x + 2, x)
[x == -2, x == -1]

You can solve equations for one variable in terms of others:

from sage.all import *
x, b, c = var('x', 'b', 'c')
solve([x**2 + b*x + c == 0], x)
[x == -1/2*b - 1/2*sqrt(b^2 - 4*c), x == -1/2*b + 1/2*sqrt(b^2 - 4*c)]

You can also solve for several variables:

from sage.all import *
x, y = var('x', 'y')
solve([x + y == 6, x - y == 4], x, y)
[[x == 5, y == 1]]