jordibc.geometric-algebra
antiwedgeclj
(antiwedge a b)Return the antiwedge product (also regressive/meet) of a and b.
Return the antiwedge product (also regressive/meet) of `a` and `b`.
basisclj
(basis signature)(basis signature start)Return basis elements of a geometric algebra with the given signature.
Return basis elements of a geometric algebra with the given signature.
commutatorclj
(commutator a b)Return a x b, the commutator product of multivectors a and b.
Return a x b, the commutator product of multivectors `a` and `b`.
def-basiscljmacro
(def-basis signature)(def-basis signature start)Create global vars with the names of the multivector basis.
Create global vars with the names of the multivector basis.
def-opscljmacro
(def-ops)Create global vars with multivector operators, replacing some core ones.
Create global vars with multivector operators, replacing some core ones.
divclj
(div a)(div a b)(div a b & more)Return a / b = a * b^-1 (if b has an inverse).
Return a / b = a * b^-1 (if `b` has an inverse).
dotclj
(dot a b)Return the dot product (inner product) of multivectors a and b.
Return the dot product (inner product) of multivectors `a` and `b`.
dualclj
(dual a)Return the dual of multivector a. Example: 2 e12 + e024 -> 2 e034 + e13.
There are other types of duals, for example ia or ai. The dual in
this function works even for degenerate algebras (algebras with i*i = 0).
Return the dual of multivector `a`. Example: 2 e12 + e024 -> 2 e034 + e13. There are other types of duals, for example i*a or a*i. The dual in this function works even for degenerate algebras (algebras with i*i = 0).
expclj
(exp a)Return exp(a), the exponentiation of multivector a.
Return exp(a), the exponentiation of multivector `a`.
fat-dotclj
(fat-dot a b)Return the "fat dot" product of multivectors a and b.
Return the "fat dot" product of multivectors `a` and `b`.
gradeclj
(grade a r)Grade-projection operator <a>_r (select only blades of the given grade r).
Example: (grade (+ e1 e2 e0245) 1) -> (+ e1 e2).
Grade-projection operator <a>_r (select only blades of the given grade `r`). Example: (grade (+ e1 e2 e0245) 1) -> (+ e1 e2).
gradesclj
(grades a)Return the grades present in multivector a.
Example: e1 + e2 + e0245 -> (1, 4).
Return the grades present in multivector `a`. Example: e1 + e2 + e0245 -> (1, 4).
infixcljmacro
(infix & expr)Evaluate the given expression expr given in infix notation.
Evaluate the given expression `expr` given in infix notation.
invclj
(inv a)Return a^-1, the inverse of multivector a if it exists.
Return a^-1, the inverse of multivector `a` if it exists.
involclj
(invol a)Return a^^, the involution of multivector a. Example: 1 + e1 -> 1 - e1.
Return a^^, the involution of multivector `a`. Example: 1 + e1 -> 1 - e1.
lcontractclj
(lcontract a b)Return the left contraction of multivectors a and b.
Return the left contraction of multivectors `a` and `b`.
multivectorclj
(multivector blades-or-num signature)Create a new multivector.
Create a new multivector.
multivector?clj
(multivector? a)Return true if a is a multivector (numbers are multivectors too).
Return true if `a` is a multivector (numbers are multivectors too).
powclj
(pow a n)Return a^n (a raised to the nth power).
Return a^n (`a` raised to the nth power).
prodclj
(prod)(prod a)(prod a b)(prod a b & more)Return a * b, the geometric product of multivectors a and b.
Return a * b, the geometric product of multivectors `a` and `b`.
projclj
(proj a b)Return P_b(a), the projection of multivector a on b.
Return P_b(a), the projection of multivector `a` on `b`.
pseudoscalar-unitclj
(pseudoscalar-unit sig)Return the pseudoscalar unit corresponding to signature sig.
Return the pseudoscalar unit corresponding to signature `sig`.
rcontractclj
(rcontract a b)Return the right contraction of multivectors a and b.
Return the right contraction of multivectors `a` and `b`.
revclj
(rev a)Return a^~, the reverse of multivector a. Example: e12 -> e21 = -e12.
Return a^~, the reverse of multivector `a`. Example: e12 -> e21 = -e12.
same-algebra?clj
(same-algebra? a b)Return true if the arguments belong to the same geometric algebra.
Return true if the arguments belong to the same geometric algebra.
scalarclj
(scalar a)Return the given multivector a as a number (if it is a scalar).
Return the given multivector `a` as a number (if it is a scalar).
scalar-prodclj
(scalar-prod a b)Return the scalar product of multivectors a and b.
Return the scalar product of multivectors `a` and `b`.
scalar?clj
(scalar? a)Return true if a is a number or a multivector with only a scalar blade.
Return true if `a` is a number or a multivector with only a scalar blade.
subclj
(sub a)(sub a b)(sub a b & more)Return -a for one argument, a - b for two, a - b - c, etc.
Return -a for one argument, a - b for two, a - b - c, etc.
sum-exp-seriesclj
(sum-exp-series a)(sum-exp-series a precision max-terms)Return exp(a) by adding the terms in its expansion in powers of a.
Return exp(a) by adding the terms in its expansion in powers of `a`.
wedgeclj
(wedge a b)Return the wedge product (also exterior/outer) of multivectors a and b.
Return the wedge product (also exterior/outer) of multivectors `a` and `b`.
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