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# name: cache
# type: cell
# rows: 3
# columns: 15
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 11
assumptions
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1257
-- Function File: A = assumptions ()
-- Function File: A = assumptions (X)
-- Function File: [V, D] = assumptions (X, 'dict')
-- Function File: L = assumptions ('possible')
List assumptions on symbolic variables.
The assumptions are returned as a cell-array of strings:
>> syms x y positive
>> syms n integer
>> assumptions
⇒ ans =
{
[1,1] = n: integer
[1,2] = x: positive
[1,3] = y: positive
}
>> f = sin(n*x);
>> assumptions(f)
⇒ ans =
{
[1,1] = n: integer
[1,2] = x: positive
}
>> assumptions(n)
⇒ ans =
{
[1,1] = n: integer
}
With the optional second argument set to the string ‘'dict'’,
return the assumption dictionaries in D corresponding to the
variables in V.
You can also get a list of possible assumptions:
>> A = assumptions('possible');
>> sprintf('%s ', A{:})
⇒ ans = real positive negative integer even odd rational finite
See also: sym, syms, assume, assumeAlso.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 39
List assumptions on symbolic variables.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
bernoulli
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 448
-- Function File: B = bernoulli (N)
-- Function File: P = bernoulli (N, X)
Return Bernoulli numbers and polynomials.
Examples:
>> bernoulli(6)
⇒ (sym) 1/42
>> bernoulli(7)
⇒ (sym) 0
Polynomial example:
>> syms x
>> bernoulli(2, x)
⇒ (sym)
2 1
x - x + ─
6
See also: euler.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
Return Bernoulli numbers and polynomials.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
catalan
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 170
-- Function File: catalan ()
Return Catalan constant.
vpa (catalan ())
⇒ (sym) 0.91596559417721901505460351493238
See also: eulergamma.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 24
Return Catalan constant.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
digits
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 479
-- Function File: N = digits ()
-- Function File: digits (N)
-- Function File: OLDN = digits (N)
Get/set number of digits used in variable precision arith.
Examples:
>> n_orig = digits(7);
>> vpa('pi')
⇒ (sym) 3.141593
>> digits(42)
>> vpa('pi')
⇒ (sym) 3.14159265358979323846264338327950288419717
>> digits(n_orig) # reset digits to saved value
See also: sym, vpa, vpasolve.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 58
Get/set number of digits used in variable precision arith.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
eulergamma
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 182
-- Function File: eulergamma ()
Return Euler-Mascheroni constant.
vpa (eulergamma ())
⇒ (sym) 0.57721566490153286060651209008240
See also: catalan.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 33
Return Euler-Mascheroni constant.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 6
evalpy
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2327
-- Function File: evalpy (CMD)
-- Function File: evalpy (CMD, X, Y, …)
Run Python code, automatically transferring results.
Examples:
>> x = -4;
>> evalpy ('y = 2*x', x)
⇒ y = -8
>> y
⇒ y = -8
You can replace ‘x’ with a new value in the Python code:
>> syms x
>> evalpy ('y = 3*x; x = -1.5; z = x**2', x)
⇒
x = -1.5000
y = (sym) 3⋅x
z = 2.2500
All arguments can be accessed as ‘i0’, ‘i1’, etc. This is useful
if they don’t have inputnames:
>> x = 10;
>> evalpy ('y = ", ".join( (str(x),str(i0),str(i1)) )', x, 5)
⇒ y = 10.0, 10.0, 5.0
If you need a variable in Python but don’t want it passed back to
Octave, put an ‘_’ (underscore) at the beginning or end.
>> x = 20;
>> evalpy ('_y = 3*x; z_ = _y/6; my = z_/2;', x)
⇒ Variables effected: my
>> _y
⇒ ??? '_y' undefined near line 1 column 1
>> z_
⇒ ??? 'z_' undefined near line 1 column 1
The final few characters of CMD effect the verbosity:
• 2 semicolons ‘;;’, very quiet, no output.
• 1 semicolon ‘;’, a one-line msg about variables assigned.
• no semicolon, display each variable assigned.
Multiline code should be placed in a cell array, see the
‘python_cmd’ documentation.
Warning: evalpy is probably too smart for its own good. It is
intended for interactive use. In your non-interactive code, you
might want ‘python_cmd’ instead.
Notes:
• if you assign to X but don’t change its value, it will not be
assigned to and will not appear in the Variables effected:"
list.
• using print is probably a bad idea. For now, use ‘dbout(x)’
to print ‘x’ to stderr which should appear in the terminal
(FIXME: currently broken on windows).
• evalpy is a bit of a work-in-progress and subject to change.
For example, with a proper IPC mechanism, you could grab the
values of X etc when needed and not need to specify them as
args.
See also: python_cmd.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 52
Run Python code, automatically transferring results.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 9
fibonacci
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 505
-- Function File: F = fibonacci (N)
-- Function File: P = fibonacci (N, X)
Return Fibonacci numbers and polynomials.
Examples:
>> fibonacci(15)
⇒ (sym) 610
>> syms n
>> fibonacci(n)
⇒ (sym) fibonacci(n)
Polynomial example:
>> syms x
>> fibonacci(10, x)
⇒ (sym)
9 7 5 3
x + 8⋅x + 21⋅x + 20⋅x + 5⋅x
See also: euler, bernouilli.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 41
Return Fibonacci numbers and polynomials.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 11
findsymbols
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 800
-- Function File: L = findsymbols (X)
Return a list (cell array) of the symbols in an expression.
The list is sorted alphabetically. *Note symvar::, for details.
If two variables have the same symbol but different assumptions,
they will both appear in the output. It is not well-defined in
what order they appear.
X could be a sym, sym array, cell array, or struct.
>> syms x y z
>> C = {x, 2*x*y, [1 x; sin(z) pi]};
>> findsymbols (C)
⇒
{
(sym) x
(sym) y
(sym) z
}
Note E, I, pi, etc are not counted as symbols.
Note only returns symbols actually appearing in the RHS of a
‘symfun’.
See also: symvar, findsym.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 59
Return a list (cell array) of the symbols in an expression.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 14
octsympy_tests
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 452
-- Function File: R = octsympy_tests ()
Run the OctSymPy tests, log results, and return true if passing.
I threw this together by modifying "__run_test_suite__.m" which is
Copyright (C) 2005-2013 David Bateman and part of GNU Octave, GPL
v3.
FIXME: once we no longer try to support Octave 3.6, drop most of
this and call "__run_test_suite({'@sym', '@symfun'}, {})" instead.
See https://savannah.gnu.org/bugs/?41215
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 64
Run the OctSymPy tests, log results, and return true if passing.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
poly2sym
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 725
-- Function File: P = poly2sym (C)
-- Function File: P = poly2sym (C, X)
Create a symbolic polynomial expression from coefficients.
If X is not specified, the free variable is set to ‘x’. C may be a
vector of doubles or syms. It can also be a cell array vector. X
may be a symbolic expression or something that converts to one.
The coefficients correspond to decreasing exponent of the free
variable.
Example:
x = sym ('x');
y = sym ('y');
poly2sym ([2 5])
⇒ (sym) 2⋅x + 5
poly2sym ({2*y 5 -3}, x)
⇒ (sym)
2
2⋅x ⋅y + 5⋅x - 3
See also: sym2poly, polyval, roots.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 58
Create a symbolic polynomial expression from coefficients.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 10
python_cmd
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 2821
-- Function File: [A, B, …] = python_cmd (CMD, X, Y, …)
Run some Python command on some objects and return other objects.
Here CMD is a string of Python code. Inputs X, Y, … can be a
variety of objects (possible types listed below). Outputs A, B, …
are converted from Python objects: not all types are possible, see
below.
Example:
>> x = 10; y = 2;
>> cmd = '(x,y) = _ins; return (x+y,x-y)';
>> [a, b] = python_cmd (cmd, x, y)
⇒ a = 12
⇒ b = 8
The inputs will be in a list called ’_ins’. The command should end
by outputing a tuple of return arguments. If you have just one
return value, you probably want to append an extra comma. Either
of these approaches will work:
>> cmd = '(x,y) = _ins; return (x+y,)';
>> a = python_cmd (cmd, x, y)
⇒ a = 12
>> cmd = '(x,y) = _ins; return x+y,';
>> a = python_cmd (cmd, x, y)
⇒ a = 12
(Python gurus will know why).
Instead of ‘return’, you can append to the Python list ‘_outs’:
>> cmd = '(x,y) = _ins; _outs.append(x**y)';
>> a = python_cmd (cmd, x, y)
⇒ a = 100
You can also pass a cell-array of lines of code. But be careful
with whitespace: its Python!
>> cmd = { '(x,) = _ins'
.. 'if x.is_Matrix:'
.. ' return (x.T,)'
.. 'else:'
.. ' return (x,)' };
The cell array can be either a row or a column vector. Each of
these strings probably should not have any newlines (other than
escaped ones e.g., inside strings). An exception might be Python
triple-quoted """ multiline strings """. FIXME: test this. It
might be a good idea to avoid blank lines as they can cause
problems with some of the IPC mechanisms.
Possible input types:
• sym objects
• strings (char)
• scalar doubles
They can also be cell arrays of these items. Multi-D cell arrays
may not work properly.
Possible output types:
• SymPy objects (Matrix and Expr at least)
• int
• float
• string
• unicode strings
• bool
• dict (converted to structs)
• lists/tuples (converted to cell vectors)
FIXME: add a py_config to change the header? The python
environment is defined in python_header.py. Changing it is
currently harder than it should be.
Note: if you don’t pass in any syms, this shouldn’t need SymPy.
But it still imports it in that case. If you want to run this w/o
having the SymPy package, you’d need to hack a bit.
See also: evalpy.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 65
Run some Python command on some objects and return other objects.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 7
sympref
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 3754
-- Function File: R = sympref ()
-- Function File: R = sympref (CMD)
-- Function File: sympref CMD
-- Function File: sympref CMD ARGS
Preferences for the OctSymPy symbolic computing package.
‘sympref’ can set or get various preferences and configurations.
The various choices for CMD and ARGS are documented below.
*Python executable* path/command:
>> sympref python '/usr/bin/python' >> sympref python 'C:\Python\python.exe' >> sympref python 'N:\myprogs\py.exe'
Default is an empty string; in which case OctSymPy just runs
‘python’ and assumes the path is set appropriately.
*Display* of syms:
>> sympref display
⇒ ans = unicode
>> syms x
>> sympref display flat
>> sin(x/2)
⇒ (sym) sin(x/2)
>> sympref display ascii
>> sin(x/2)
⇒ (sym)
/x\
sin|-|
\2/
>> sympref display unicode
>> sin(x/2)
⇒ (sym)
⎛x⎞
sin⎜─⎟
⎝2⎠
>> sympref display default
By default OctSymPy uses the unicode pretty printer to display
symbolic expressions. If that doesn’t work (e.g., if you see ‘?’
characters) then try the ‘ascii’ option.
*Communication mechanism*:
>> sympref ipc
⇒ ans = default
The default will typically be the ‘popen2’ mechanism which uses a
pipe to communicate with Python and should be fairly fast. If that
doesn’t work, try ‘sympref display system’ which is much slower, as
a new Python process is started for each operation (many commands
use more than one operation). Other options for ‘sympref ipc’
include:
• ‘sympref ipc popen2’: force popen2 choice (e.g., on Matlab
were it would not be the default).
• ‘sympref ipc system’: construct a long string of the command
and pass it directly to the python interpreter with the
‘system()’ command. This typically assembles a multiline
string for the commands, except on Windows where a long
one-line string is used.
• ‘sympref ipc systmpfile’: output the python commands to a
‘tmp_python_cmd.py’ file and then call that [for debugging,
may not be supported long-term].
• ‘sympref ipc sysoneline’: put the python commands all on one
line and pass to ‘python -c’ using a call to ‘system()’. [for
debugging, may not be supported long-term].
*Reset*: reset the SymPy communication mechanism. This can be
useful after an error occurs and the connection with Python becomes
confused.
>> sympref reset
*Snippets*: when displaying a sym object, we quote the SymPy
representation (or a small part of it):
>> syms x
>> y = [pi x];
>> sympref snippet on
>> y
⇒ y = (sym 1×2 matrix) “...([[pi, Symbol('x')]])”
[π x]
>> sympref snippet off
>> y
⇒ y = (sym) [π x] (1×2 matrix)
>> sympref snippet default
*Default precision*: control the number of digits used by
variable-precision arithmetic (see also the *note digits::
command).
>> sympref digits % get
⇒ ans = 32
>> sympref digits 64 % set
>> sympref digits default
Report the *version* number:
>> sympref version
⇒ 2.2.4
See also: sym, syms.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 56
Preferences for the OctSymPy symbolic computing package.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 4
syms
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 1337
-- Function File: syms X
-- Function File: syms X Y …
-- Function File: syms F(X)
-- Function File: syms X ASM
-- Function File: syms X ASM ASM2 …
-- Function File: syms
Create symbolic variables and symbolic functions.
This is a convenience function. For example:
>> syms x y z
instead of:
>> x = sym('x');
>> y = sym('y');
>> z = sym('z');
The last arguments can provide one or more assumptions (type or
restriction) on the variable (*note sym::).
>> syms x y z positive
>> syms n positive even
Symfuns represent abstract or concrete functions. Abstract symfuns
can be created with ‘syms’:
>> syms f(x)
If ‘x’ does not exist in the callers workspace, it is created as a
*side effect* in that workspace.
Called without arguments, ‘syms’ displays a list of all symbolic
functions defined in the current workspace.
Caution: On Matlab, you may not want to use ‘syms’ within
functions. In particular, if you shadow a function name, you may
get hard-to-track-down bugs. For example, instead of writing ‘syms
alpha’ use ‘alpha = sym('alpha')’ in functions.
[https://www.mathworks.com/matlabcentral/newsreader/view_thread/237730]
See also: sym.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 49
Create symbolic variables and symbolic functions.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 3
vpa
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 697
-- Function File: Y = vpa (X)
-- Function File: Y = vpa (X, N)
Create a variable-precision floating point number.
X can be a string, a sym or a double. Example:
>> x = vpa('1/3', 32)
⇒ x = (sym) 0.33333333333333333333333333333333
>> a = sym(1)/3;
>> x = vpa(a, 32)
⇒ x = (sym) 0.33333333333333333333333333333333
Be careful when creating a high-precision float from a double as
you will generally only get 15 digits:
>> vpa(1/3, 32)
⇒ (sym) 0.33333333333333331482961625624739
If N is omitted it defaults to the current value of ‘digits()’.
See also: sym, vpasolve, digits.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 50
Create a variable-precision floating point number.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 8
vpasolve
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 458
-- Function File: Y = vpasolve (E)
-- Function File: Y = vpasolve (E, X)
-- Function File: Y = vpasolve (E, X, X0)
Numerical solution of a symbolic equation.
Variable-precision numerical solution of the equation E for
variable X using initial guess of X0.
Example:
>> syms x
>> eqn = exp(x) == x + 2;
>> vpasolve(eqn, x, 0.1)
⇒ (sym) 1.1461932206205825852370610285214
See also: vpa.
# name: <cell-element>
# type: sq_string
# elements: 1
# length: 42
Numerical solution of a symbolic equation.
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