diff options
Diffstat (limited to 'src/algebra/carten.spad.pamphlet')
| -rw-r--r-- | src/algebra/carten.spad.pamphlet | 12 |
1 files changed, 6 insertions, 6 deletions
diff --git a/src/algebra/carten.spad.pamphlet b/src/algebra/carten.spad.pamphlet index 064b0865..8b00959a 100644 --- a/src/algebra/carten.spad.pamphlet +++ b/src/algebra/carten.spad.pamphlet @@ -40,19 +40,19 @@ GradedModule(R: CommutativeRing, E: AbelianMonoid): Category == ++ of a given degree form an R-module. 0: constant -> % ++ 0 denotes the zero of degree 0. - _*: (R, %) -> % + *: (R, %) -> % ++ r*g is left module multiplication. - _*: (%, R) -> % + *: (%, R) -> % ++ g*r is right module multiplication. - _-: % -> % + -: % -> % ++ -g is the additive inverse of g in the module of elements ++ of the same grade as g. - _+: (%, %) -> % + +: (%, %) -> % ++ g+h is the sum of g and h in the module of elements of ++ the same degree as g and h. Error: if g and h ++ have different degrees. - _-: (%, %) -> % + -: (%, %) -> % ++ g-h is the difference of g and h in the module of elements of ++ the same degree as g and h. Error: if g and h ++ have different degrees. @@ -171,7 +171,7 @@ CartesianTensor(minix, dim, R): Exports == Implementation where ++ then \spad{r} is a rank 4 tensor given by ++ \spad{r(i,j,k,l) = s(i,j)*t(k,l)}. - "*": (%, %) -> % + *: (%, %) -> % ++ s*t is the inner product of the tensors s and t which contracts ++ the last index of s with the first index of t, i.e. ++ \spad{t*s = contract(t,rank t, s, 1)} |