Symbolic computation

This package provides a light-weight wrapper to support use of SymPy. It generalizes some common functions so that they can accept numerical or Symbolic arguments.

If SymPy is not installed then only the standard numeric operations are supported.

cos(theta)

Generalized cosine function

Parameters

θ (float or symbolic) – argument

Returns

cos(θ)

Return type

float or symbolic

>>> from spatialmath.base.symbolic import *
>>> theta = symbol('theta')
>>> cos(theta)
cos(theta)
>>> cos(0.5)
0.8775825618903728

Seealso

sympy.cos()

det(x)

Symbolic determinant

Parameters

m – matrix

Returns

determinant

Return type

ndarray with symbolic elements

  File "/opt/hostedtoolcache/Python/3.7.17/x64/lib/python3.7/site-packages/sympy/simplify/simplify.py", line 604, in simplify
    original_expr = expr = collect_abs(signsimp(expr))
  File "/opt/hostedtoolcache/Python/3.7.17/x64/lib/python3.7/site-packages/sympy/simplify/radsimp.py", line 606, in collect_abs
    return expr.replace(
AttributeError: 'NoneType' object has no attribute 'replace'

Note

Converts to a SymPy Matrix and then back again.

issymbol(var)

Test if variable is symbolic

Parameters

var (Any) – variable to test

Returns

whether variable is symbolic

Return type

bool

>>> from spatialmath.base.symbolic import *
>>> theta = symbol('theta')
>>> issymbol(theta)
True
>>> issymbol(3.4)
False

negative_one()

Symbolic constant: negative one

Returns

-1

Return type

symbolic

>>> from spatialmath.base.symbolic import *
>>> x = symbol('x')
>>> negative_one()
-1
>>> negative_one() * x
-x

Seealso

sympy.S.NegativeOne()

one()

Symbolic constant: one

Returns

1

Return type

symbolic

>>> from spatialmath.base.symbolic import *
>>> x = symbol('x')
>>> one()
1
>>> one() * x
x

Seealso

sympy.S.One()

pi()

Symbolic constant: pi

Returns

π

Return type

symbolic

>>> from spatialmath.base.symbolic import *
>>> import math
>>> sin(pi())
0
>>> sin(math.pi)
1.2246467991473532e-16

Seealso

sympy.S.Pi()

simplify(x)

Symbolic simplification

Parameters

x (symbolic) – expression to simplify

Returns

-1

Return type

symbolic

>>> from spatialmath.base.symbolic import *
>>> x = symbol('x')
>>> y = (x - 1) * (x + 1) - x ** 2
>>> y
-x**2 + (x - 1)*(x + 1)
>>> simplify(y)
-1

Seealso

sympy.simplify()

sin(theta)

Generalized sine function

Parameters

θ (float or symbolic) – argument

Returns

sin(θ)

Return type

float or symbolic

>>> from spatialmath.base.symbolic import *
>>> theta = symbol('theta')
>>> sin(theta)
sin(theta)
>>> sin(0.5)
0.479425538604203

Seealso

sympy.sin()

sqrt(v)

Generalized sqrt function

Parameters

v (float or symbolic) – argument

Returns

√ v

Return type

float or symbolic

>>> from spatialmath.base.symbolic import *
>>> x = symbol('x')
>>> sqrt(x ** 2)
Abs(x)
>>> sqrt(4)
2.0

Seealso

sympy.sqrt()

symbol(name, real=True)

Create symbolic variables

Parameters

• name (str) – symbol names

• real (bool, optional) – assume variable is real, defaults to True

Returns

SymPy symbols

Return type

sympy

>>> from spatialmath.base.symbolic import *
>>> theta = symbol('theta')
>>> theta
theta
>>> theta, psi = symbol('theta psi')
>>> theta
theta
>>> psi
psi
>>> q = symbol('q_:6')
>>> q
(q_0, q_1, q_2, q_3, q_4, q_5)

Note

In Jupyter symbols are pretty printed.

• symbols named after greek letters will appear as greek letters

• underscore means subscript as it does in LaTex, so the symbols q

above will be subscripted.

Seealso

sympy.symbols()

tan(theta)

Generalized tangent function

Parameters

θ (float or symbolic) – argument

Returns

tan(θ)

Return type

float or symbolic

>>> from spatialmath.base.symbolic import *
>>> theta = symbol('theta')
>>> tan(theta)
tan(theta)
>>> tan(0.5)
0.5463024898437905

Seealso

sympy.cos()

zero()

Symbolic constant: zero

Returns

0

Return type

symbolic

>>> from spatialmath.base.symbolic import *
>>> x = symbol('x')
>>> zero()
0
>>> x + zero()
x

Seealso

sympy.S.Zero()