Implies(And(d1::even, d2::odd), d1+d2 <= 9);

The prettyprinted output of this will be in standard logical notation.

Try this:

TypeTools:-AddType(
    special_polynomial,
    (p, x::name)-> 
    local 
        X, k:= 0,
        T:= subsindets(
            p, 
            identical(x)^{constant, And(name, Not({identical(x), X[posint]}))}, 
            ()-> X[++k]
        )
    ;
        type(T, polynom(anything, {x} union indets(T, X[posint])))
);

Usage:

type(expr, special_polynomial(x));

I don't think that your way is good, for two reasons:

• I don't think that you understand what Maple's type algebraic is. Look up ?type,algebraic. Surely you don't want x^sin(x) + 1 to be considered a special polynomial.
• The scanning by remove is only through the top level of an expression--the terms in this case. Looking within the terms requires the deeper scan provided by subsindets (or evalindets). For example, your procedure would not call 3*x^(1/2) + 1 a special polynomial because it doesn't see the x^(1/2) because of the 3.

Also note that Pi, sqrt(3), etc., are type constant but not type numeric.

The operators numer and denom are mathematical, not purely syntactic like lhs and rhs. It's easy enough to write a syntactic operator to do what you want:

Apparent_Numer_Denom:= (e::`*`)-> 
    ((D,N)-> (N,1/D))(selectremove(type, e, anything^negative))
:
Apparent_Numer_Denom(expr);
 

ProductOfDiagonal:= (M::Matrix)-> mul(ArrayTools:-Diagonal(M));

Trying to guess your next Question, the sum of the k-wise products of the diagonal entries is

SumKwiseProducts:= (M::Matrix, k::nonnegint)-> 
    add(mul~(combinat:-choose([seq](ArrayTools:-Diagonal(M)), k)))
:

plots:-odeplot(sol, [t, diff(x(t), t)], t= 0..20);

mySumOfMatrixDiagonal:= (M::Matrix('square'))-> add(M[k,k]^2, k= 1..upperbound(M)[1]):

For each k, y is a surface, not a curve, so use plot3d:

y:= k*x*sqrt(z*(1-z)):
plot3d(
    [seq([x,y,z], k= 5..100, 5)], x= 0..1, z= 0..1, 
    color= [seq(COLOR(HUE, .85*(k-5)/95), k= 5..100, 5)], 
    transparency= .15
);

Your answer[1] is a set, not an equation. Sets don't have right-hand sides. Here are four ways to proceed:

Map over the set:

rhs~(answer[1]);

Extract the first (and only) element from the set:

rhs(answer[1][1]);

Extract all elements from the set (this only works because there's only one element):

rhs(answer[1][]);

Forget about rhs; use eval instead:

eval(U__T2N, answer[1]);

The eval method is probably the one most commonly used by experienced Maple users.

The third form is equivalent to the first form under complex evaluation with appropriate adjustments of the contants of integration. And the second form can be obtained as a limit of the third form. For example,
 

Download EulerODE.mw

I don't know all the details of how Grid works, but intuitively Grid:-Set(arg1) seems unnecessary to me, and it seems like it would consume a lot of memory.

If one were required to use Grid:-Set(arg1), that would seem to me to be contrary to the whole idea of dividing the work among multiple processes.

Where you have blocks= [u,v], it should be 

blocks= [[u, v]]

Here is your complete code in the abbreviated "jet" notation:

restart:
DA:= DifferentialAlgebra:  DAT:= DA:-Tools:
R:= DA:-DifferentialRing('blocks'= [[u,v]], 'derivations'= [t]):
p:= u[t$3]*v[t] - u[t]*v[t$3]:
q:= v[t$3]^2*(v[t]*u[t$2] - v[t$2]*u[t]):
s:= DAT:-DifferentialPrem(p, q, R);
           s := 1, -u[t] v[t, t, t] + u[t, t, t] v[t]

In addition to sum not working for this, you've made a mistake by indexing the last row as 9. It's actually 10, but you do not need to index it at all. The sum that you want is simply

m1[2.., 1] . m1[2.., 2]

It is expressed above as the dot product of two vectors, i.e., a single operation that does the sum of the elementwise product of two vectors.

You simply need to switch Re with seq:

The following will work for any GridGraph:

restart:
GT:= GraphTheory:
G:= GT:-SpecialGraphs:-GridGraph(3,3):
GT:-DrawGraph(
    GT:-RelabelVertices(
        G, 
        sort(
            -sort(
                GT:-Vertices(G), 
                key= (v-> local p:= parse(v); [p[2], -p[1]]), 
                output= permutation
            ), 
            output= permutation
        )
    ), 
    stylesheet= "legacy"
);

The culprit is a remember table in procedure SumTools:-DefiniteSum:-ClosedForm. So a workaround is to use 

forget(SumTools);

before the second call to sum.

But since remember tables don't work correctly with mutable containers (such as Vectors), I'd recommend not using sum at all when the summand contains vector entries.