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On leibniz write sage into a command prompt, this starts the sage interactive shell.
Most sage commands work here, for example:
- Calculate the squareroot of 2017!
- Caltulate the 4th root of 2017!
- Calculate the 2017^6!
- What's the remaider of 123*321 divided by 11?
Text completion and help
Sage can complete your commands, try the following:
V = Vec[press TAB]
Sage completes the command to Vector, and offers additional options. Complete it to match the following:
V = VectorSpace(QQ,3)
This way V will be the 3 dimensional vector space over the rational field.
Now write V. and press TAB. Now we can see all the possible operations with V. Writing a questionmark at the end of a command gives a detailed description of the command. For example:
- Go to the sage notebook page: notebook
- Login with the username and password provided.
- Top right Settings change your password.
- After logging in again with the new password, you can open a new notebook with New Worksheet.
- Name it something like Practical10
- You can write any sage command in the cells, even multiple ones, for example:
A = Matrix([[1, 1], [1, 0]]) B = Matrix([[-2, 0], [-1, 1]])
- Run the commands with SHIFT + ENTER. The commands run one after the other.
- Try writing just A or B in a cell and run it. Then try A*B.
- Let Y be your year of birth, M the month, and D the day, create these variables.
- How much is Y divided by D? Associate this value with the b variable.
- Let r be the remainder of Y / M.
- What's the difference r - b?
Sage functions, methods
- Is 2017 a prime? (use the is_prime() function)
- Were you born on a prime day? (use the D variable!)
- Solve the equation D*x^2 + M*x - b*r = 0 using the solve(fv, variable) function! (x needs to be a symbolic variable!)
- Solve the equation numerically! Use the find_root(fv == 0, min, max) function, where min and max defines an interval where Sage looks for the solution.
- Solve the above equation symbolically (make D, M, b, r symbolic variables, then use solve)!
- Differentiate the function sin(x)cos(x)x^2.
- Integrate the previous function.
- Calculate the limit of (1 + 3/n)^4n, if n->oo
- Let f be the following function: f = (x+2*y)^3
- Substitute 3 into x; then 4 into x and 2 into y. What's the result? ( use the subs() method of f)
- Expand f! (expand())
- Using the above, calculate the Taylor series of sin(x)cos(x)x^2 up until the 4th member. (you can differentiate and integrate a function f by f.diff(x))
Plotting with Sage (plot)
- Plot a cosine curve from 0 to 4*pi!
- Plot the (x-2)^2 + 3 polynomial from -2 to 4, color it green!
- Plot next to the previous one (using the show function) the function x^3-3*x + 6 in red!
- Plot a circle: cirlce((coordinates of the center), radius, optional). The "optional" can be: color, aspect_ratio=True so that the ratio of the x and y axis are kept, otherwise we might get an ellipse.