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Functions and commands 325
Series Returns the series expansion of an expression in the vicinity of
a given equality variable. With the optional third and fourth
arguments you can specify the order and direction of the
series expansion. If no order is specified the series returned is
fifth order. If no direction is specified, the series is
bidirectional.
series(Expr,Equal(var=limit_point),[Orde
r],[Dir(1,0,-1)])
Example:
series((x^4+x+2)/(x^2+1),x=0,5) gives 2+x-2x^2-
x^3+3x^4+x^5+x^6*order_size(x)
Summation With two arguments, returns the discrete antiderivative of the
expression with respect to the variable.
sum(Expr,Var)
With four arguments, returns the discrete sum of the
expression with respect to the variable from a to b.
sum(Expr,Var,VarMin(a),VarMax(b))
Example:
sum(n^2,n,1,5) gives 55
Differential
Curl Returns the rotational curl of a vector field, defined by:
curl([A,B,C],[x,y,z])=[dC/dy-dB/dz,dA/dz-dC/dx,dB/dx-
dA/dy].
curl(Lst(A,B,C),Lst(x,y,z))
Example:
curl([2*x*y,x*z,y*z],[x,y,z]) gives [z-x,0,z-
2*x]
Divergence Returns the divergence of a vector field, defined by:
divergence([A,B,C],[x,y,z])=dA/dx+dB/dy+dC/dz.
divergence(Lst(A,B,C),Lst(x,y,z))
Example:
divergence([x^2+y,x+z+y,z^3+x^2],[x,y,z])
gives 2*x+3*z^2+1