Informatics1-2017/Practice10
A MathWikiből
(Változatok közti eltérés)
(→Tasks) |
|||
(egy szerkesztő 4 közbeeső változata nincs mutatva) | |||
42. sor: | 42. sor: | ||
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: | 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: | ||
<python> | <python> | ||
− | V. | + | V.basis? |
</python> | </python> | ||
Try it: | Try it: | ||
<python> | <python> | ||
− | V. | + | V.basis() |
</python> | </python> | ||
54. sor: | 54. sor: | ||
* Login with the username and password provided. | * 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''' |
− | === | + | === Introduction === |
− | * | + | * You can write any sage command in the cells, even multiple ones, for example: |
<python> | <python> | ||
A = Matrix([[1, 1], [1, 0]]) | A = Matrix([[1, 1], [1, 0]]) | ||
B = Matrix([[-2, 0], [-1, 1]]) | B = Matrix([[-2, 0], [-1, 1]]) | ||
</python> | </python> | ||
− | * '''SHIFT + ENTER''' | + | * 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'''. |
− | == | + | == Tasks == |
− | === | + | === Using variables === |
− | # | + | # 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 [https://en.wikipedia.org/wiki/Taylor_series 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. |
− | + | ||
− | + |
A lap jelenlegi, 2017. november 13., 15:01-kori változata
Tartalomjegyzék |
Using Sage
Sage server
If your browser finds the certificate untrustworthy, accept it manually!
Public
From home (if you want to install, optional)
http://doc.sagemath.org/html/en/installation/index.html
Command line
On leibniz write sage into a command prompt, this starts the sage interactive shell.
Most sage commands work here, for example:
23^19
Tasks
- 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:
V.basis?
Try it:
V.basis()
Sage notebook
- 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
Introduction
- 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.
Tasks
Using variables
- 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.