Ref.
Derivative of abs
fricas
s1:=D(abs(x),x)
Type: Expression(Integer)
fricas
D(s1,x)
Type: Expression(Integer)
fricas
limit(abs(x)/x,x=0,"right")
Type: Union(OrderedCompletion
?(Expression(Integer)),
...)
fricas
limit(abs(x)/x,x=0,"left")
Type: Union(OrderedCompletion
?(Expression(Integer)),
...)
An approximation to signum
fricas
D(tanh(a*x),x)
Type: Expression(Integer)
fricas
limit(%,a=%plusInfinity)
Type: Union("failed",...)
Patterns for derivatives
fricas
Abs:=operator('Abs)
fricas
D(abs(x),x)
Type: Expression(Integer)
fricas
signum:=operator('signum)
fricas
diracDelta:=operator('diracDelta)
fricas
signum(x)
Type: Expression(Integer)
fricas
D(signum(x),[x,x])
Type: Expression(Integer)
fricas
diff1:=rule
signum(x) == Abs(x)/x
D(Abs(x),x) == signum(x) + 2*x*diracDelta(x)
D(signum(x),x) == 2*diracDelta(x)
Type: Ruleset(Integer,Integer,Expression(Integer))
fricas
diff(x,y)==diff1 D(x,y)
Type: Void
fricas
diff(Abs(x),x)
fricas
Compiling function diff with type (Expression(Integer),Variable(x))
-> Expression(Integer)
Type: Expression(Integer)
fricas
diff(Abs(x)/x,x)
Type: Expression(Integer)
Adding the singular part of the derivative
fricas
diff(f,x) == D(f,x)+(limit(f,x=0,"right")-limit(f,x=0,"left"))::EXPR(INT)*diracDelta(x)
Compiled code for diff has been cleared.
1 old definition(s) deleted for function or rule diff
Type: Void
fricas
diff(abs(x),x)
fricas
Compiling function diff with type (Expression(Integer),Variable(x))
-> Expression(Integer)
Type: Expression(Integer)
fricas
diff(%,x)
Type: Expression(Integer)
fricas
signum(x)==abs(x)/x
Type: Void
fricas
diff(signum(x),x)
fricas
Compiling function signum with type Variable(x) -> Expression(
Integer)
Type: Expression(Integer)
fricas
integrate(signum(x),x)
Type: Union(Expression(Integer),...)