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- "File VECTOR.MTH, copyright (c) 1990-2000 by Texas Instruments Incorporated"
-
- i_:=[1,0,0]
-
- j_:=[0,1,0]
-
- k_:=[0,0,1]
-
- OUTER(v,w):=VECTOR([v SUB n_],n_,DIM(v)) . [w]
-
- KRONECKER(i,j):=IF(i=j,1,0)
-
- ADJOIN_ELEMENT(e,v):=ADJOIN(e,v)
-
- MATRIX?(a,r_):=VECTOR?(a) AND EVERY(VECTOR?(r_),r_,a)
-
- APPEND_COLUMNS Args:=IF(DIM(Args)=1 AND VECTOR?(Args SUB 1) AND EVERY(MATRIX?(~
- a_),a_,Args SUB 1),APPEND(VECTOR(a_`,a_,Args SUB 1))`,APPEND(VECTOR(a_`,a_,Arg~
- s))`)
-
- PARTITION(v,n,d):=IF(NUMBER(d),VECTOR(VECTOR(v SUB m_,m_,n_,n_+n-1),n_,1,1+d*F~
- LOOR(DIM(v)-n,d),d),PARTITION(v,n,n))
-
- MINOR(a,i,j):=DELETE(DELETE(a,i)`,j)`
-
- SWAP_ELEMENTS(v,i,j):=VECTOR(IF(m_=i,v SUB j,IF(m_=j,v SUB i,v SUB m_)),m_,DIM~
- (v))
-
- SCALE_ELEMENT(v,i,s):=VECTOR(IF(m_=i,s*v SUB i,v SUB m_),m_,DIM(v))
-
- SUBTRACT_ELEMENTS(v,i,j,s:=1):=VECTOR(IF(m_=i,v SUB i-s*v SUB j,v SUB m_),m_,D~
- IM(v))
-
- FORCE0(a,i,j,p):=VECTOR(IF(m_=i,a SUB i-a SUB i SUB j/a SUB p SUB j*a SUB p,a ~
- SUB m_),m_,DIM(a))
-
- PIVOT(a,i,j):=VECTOR(IF(m_<=i,a SUB m_,a SUB m_-a SUB m_ SUB j/a SUB i SUB j*a~
- SUB i),m_,DIM(a))
-
- MATPROD(a,b,i,j):=SUM(a SUB i SUB n_*b SUB n_ SUB j,n_,1,DIM(b))
-
- COFACTOR(a,i,j):=COS(pi*(i+j))*DET(MINOR(a,i,j))
-
- ADJOINT(a):=VECTOR(VECTOR(COFACTOR(a,m_,n_),m_,DIM(a)),n_,DIM(a))
-
- EXACT_EIGENVECTOR(a,mu):=SOLUTIONS(VECTOR(SUM((a SUB m_ SUB n_-mu*KRONECKER(m_~
- ,n_))*APPEND("x",n_),n_,1,DIM(a)),m_,DIM(a)),VECTOR(APPEND("x",n_),n_,1,DIM(a)~
- ))
-
- APPROX_EIGENVECTOR(a,mu):=SIGN(ROW_REDUCE(a-mu*IDENTITY_MATRIX(DIM(a)),VECTOR(~
- 3000*COS(pi*m_)/m_,m_,DIM(a)))` SUB (DIM(a)+1))
-
- cylindrical:=[[r,theta,z],[1,r,1]]
-
- spherical:=[[r,theta,phi],[1,r*SIN(phi),r]]
-
- JACOBIAN(u,alpha):=VECTOR(GRAD(u SUB m_,alpha),m_,DIM(u))
-
- COVARIANT_METRIC_TENSOR(a):=a` . a
-
- GEOMETRY_MATRIX(alpha,g):=[alpha,VECTOR(SQRT(g SUB m_ SUB m_),m_,DIM(g))]