9.5. Monomials

A monomial is defined as a product of tensors such that it cannot be further reduced into products with different dummies. The function BreakInMonomials decomposes an arbitrary expression in monomials with (inert) head Monomial.

We break this expressions in monomials. Note that scalars are left outside:

In[949]:=

7r[]^2T[a, b, c] U[-b, -c, -e] v[e] T[f, g, h] v[-g] v[-h]

Out[949]=

7 r_^^2 T_   ^abc T_   ^fgh U_bce^    v_ ^e v_g^ v_h^

In[950]:=

BreakInMonomials[%]

Out[950]=

7 Monomial[T_   ^abc U_bce^    v_ ^e] Monomial[T_   ^fgh v_g^ v_h^ ] r_^^2

Now for example each monomial could be canonicalized independently:

In[951]:=

%/.expr_Monomial:→ToCanonical[expr]

Out[951]=

7 Monomial[T_   ^abc U_bce^    v_ ^e] Monomial[T_   ^fgh v_g^ v_h^ ] r_^^2

Monomial                Head for a monomial expression
BreakInMonomials        Separate a term in monomials

Monomials.

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