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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

2.4 Basic Algebra and Calculus

Sage can perform various computations related to basic algebra and calculus: for example, finding solutions to equations, differentiation, integration, and Laplace transforms.

See the Sage Constructions documentation for more examples.

In all these examples, it is important to note that the variables in the functions are defined to be var(...).

As an example:

u = var('u')
diff(sin(u), u)
cos(u)
cos(u)
# Define the variable
u = var('u')

# Differentiate sin(u) with respect to u
diff_sin_u = diff(sin(u), u)

# Display the result
diff_sin_u

If you get a NameError, check to see if you misspelled something, or forgot to define a variable with var(...).