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i1 = new1, i2 = new2, …, <Unsimplified>)
subsop returns a modified copy of the object,
but does not change the object itself.
subsop(object, i = new) replaces the operand
new. Operands are specified in
the same way as with the function
i may be an integer
or a list of integers. E.g.,
subsop(object, [j, k] = new) replaces
op(op(object, j), k). Cf. Example 2. In contrast to
op, ranges cannot
be used in
subsop to specify more than one operand
to replace. Several substitution equations have to be specified instead.
If several operands are to be replaced, the specified substitutions are processed in sequence from left to right. Each substitution is carried out and the result is processed further with the next substitution. The intermediate objects are not simplified.
Operands of expression sequences can be replaced by
Such objects are not flattened.
Note that the order of the operands may change by replacing operands and evaluating the result. Cf. Example 4.
FAIL is returned if an operand cannot be
subsop(object) is allowed; it returns
the object without modifications.
We demonstrate how to replace one or more operands of an expression:
x := a + b: subsop(x, 2 = c)
subsop(x, 1 = 2, 2 = c)
Also the 0-th operand of an expression (the “operator”) can be replaced:
subsop(x, 0 = _mult)
x itself was not affected by
The following call specifies the suboperand
a list of integers:
subsop([a, b, f(c)], [3, 1] = x)
This example demonstrates the effect of simplification. The
following substitution replaces the first operand
a by 2.
The result simplifies to 3:
subsop(a + 1, 1 = 2)
Unsimplified suppresses the simplification:
subsop(a + 1, 1 = 2, Unsimplified)
The next call demonstrates the difference between simplification and evaluation.
After substitution of
sin is not evaluated, i.e., the
body of the system function
sin is not executed:
subsop(sin(x), 1 = PI)
sin simplifies the result:
The order of operands may change by substitutions. Substituting
b changes the internal order of
the terms in
x := a + b + c: op(x)
x := subsop(x, 2 = z): op(x)
Any MuPAD® object
Integers or lists of integers
Arbitrary MuPAD objects
As the last step of a substitution, the modified object is simplified (however, not evaluated). This option suppresses this final simplification. Cf. Example 3.
Input object with replaced operands or
subsop, it is sufficient
to handle the cases
i = new).
The case where the position of the operand to be replaced is
given by a list is always handled recursively: First,
op is called with the
list bar the last element to find the object to substitute in (using
the overloading of
present, storing all the intermediate results), then the substitution
is performed on that sub-object (using the overloading of
subsop(subobj, i = new)). The result is
substituted into the last-but-one result of the recursive
op call, again respecting
any overloading of
subsop, and so on up to the
front of the list.