subsex

Extended substitution

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Syntax

subsex(f, old = new, <Unsimplified>)
subsex(f, old1 = new1, old2 = new2, …, <Unsimplified>)
subsex(f, [old1 = new1, old2 = new2, …], <Unsimplified>)
subsex(f, {old1 = new1, old2 = new2, …}, <Unsimplified>)
subsex(f, table(old1 = new1, old2 = new2, …), <Unsimplified>)
subsex(f, s1, s2, …, <Unsimplified>)

Description

subsex(f, old = new) returns a copy of the object f in which all expressions matching old are replaced by the value new.

subsex returns a modified copy of the object, but does not change the object itself.

subsex(f, old = new) searches f for subexpressions matching old. Each such subexpression is replaced by new.

Unlike the subs function, subsex replaces “incomplete” subexpressions. For example, subsex(a + b + c, b + c = d) replaces b + c but subs(a + b + c, b + c = d) does not replace b + c. In general, combinations of the operands of the n-ary “operators” +, *, and, _exprseq, intersect, or, _lazy_and, _lazy_or, and union can be replaced. In particular, partial sums and partial products can be replaced. Note that these operations are assumed to be commutative, e.g., subsex(a*b*c, a*c = new) does replace the partial product a*c by new. See Example 1 and Example 2. However, the advantage of subs over subsex is that subs is much faster.

subsex additionally replaces powers with the same base, if the exponent of the expression is an integer multiple of the replacement power, e.g. like in subsex(a^4, a^2 = new). This rule also matches inverted expressions like in subsex(1/sqrt(x), sqrt(x)=new), which is internally equivalent to subsex(x^(-1/2), x^(1/2)=new). Cf. Example 3.

The call subsex(f, old1 = new1, old2 = new2, ...) invokes a “sequential substitution”. See the subs help page for details.

The call subsex(f, [old1 = new1, old2 = new2, ...]) invokes a “parallel substitution”. See the subs help page for details.

The call subsex(f, s1, s2, ...) describes the most general form of substitution which may combine sequential and parallel substitutions. This call is equivalent to subsex(... subsex(subsex(f, s1), s2), ...). Depending on the form of s1, s2, , sequential or parallel substitutions are carried out in each step. An example can be found on the subs help page.

After substitution, the result is not evaluated. Use the function eval to enforce evaluation. Cf. Example 5.

Operands of expression sequences can be replaced by subsex. Such objects are not flattened. Cf. Example 6.

The call subsex(f) is allowed; it returns f without modifications.

Examples

Example 1

We demonstrate some simple substitutions; subsex finds and replaces partial sums and products:

subsex(a + b + c, a + c = x)

subsex(a*b*c, a*c = x)

subsex(a * (b + c) + b + c, b + c = a)

subsex(a + b*c*d + b*d, b*d = c);

Example 2

We replace subexpressions inside a symbolic union of sets:

subsex(a union b union c, a union b = w)

The same can be achieved by using the functional equivalent _union of the operator union:

subsex(_union(a, b, c), _union(a, b) = w)

For details on substitution functions in MuPAD®, please see Modify Subexpressions. For details on expression trees, please see Visualize Expression Trees.

Example 3

subsex replaces powers with with the same base, if the exponent of the expression is an integer multiple of the replacement power:

subsex(1/a^4, a^2 = X)

This holds even for exponents which are expressions:

subsex(1/a^(6*x), a^(2*x) = X)

1/sqrt(x) is internally x^(-1/2), so the replacement of sqrt(x) which is internally x^(1/2) works, too:

subsex(1/sqrt(n), sqrt(n) = X)

Example 4

subsex is often useful to convert the output of one command into a form required by the next one. As an example, we compute the Laplace transform of the two-dimensional ODE

,

,

and transform the result into a form suitable for calling solve by replacing the unknown Laplace transforms by symbolic names:

xfrm1 := laplace(x'(t) = x(t) + 2*y(t), t, s);
xfrm2 := laplace(y'(t) = 5*x(t) + 2*y(t), t, s)

For readability, we give names to both substitutions:

sub_x := laplace(x(t),t,s) = X:
sub_y := laplace(y(t),t,s) = Y:
Leqn1 := subs(xfrm1, sub_x, sub_y, x(0) = 1);
Leqn2 := subs(xfrm2, sub_x, sub_y, y(0) =-2)

solve({Leqn1, Leqn2}, {X, Y})

Example 5

The result of subsex is not evaluated. In the following call, the identifier sin is not replaced by its value, i.e., by the procedure defining the behavior of the system's sine function. Consequently, sin(2*PI) is not simplified to 0 by this procedure:

subsex(sin(2*x*y), x*y = PI)

The function eval enforces evaluation:

eval(subsex(sin(2*x*y), x*y = PI))

Example 6

Operands of expression sequences can be substituted. Note that sequences need to be enclosed in brackets:

subsex((a, b, a*b*c), a*b = x)

Example 7

The option Unsimplified suppresses simplification:

subsex(2 + a + b, a + b = 0, Unsimplified)

Parameters

f

An arbitrary MuPAD object

old, old1, old2, …

Arbitrary MuPAD objects

new, new1, new2, …

Arbitrary MuPAD objects

s1, s2, …

Either equations old = new, or lists or sets of such equations, or tables whose entries are interpreted as such equations.

Options

Unsimplified

Prevents simplification of the returned object after substitution

As the last step of a substitution, the modified object is simplified (however, not evaluated). This option suppresses this final simplification. See Example 7.

Return Values

Copy of the input object with replaced operands.

Overloaded By

f

See Also

MuPAD Functions