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TTYOFF:TRUE$
DIMENSION(W) := BLOCK(/* W is an equation or a list of
equations with an indeterminate on the left and a product of
powers of MASS, LENGTH, TYME, TEMPERATURE, and CHARGE on
the right. Globally establishes corresponding row(s) for
exponent matrices, returning DONE. */
[V, ACTUAL, VALID],
VALID: '[MASS, LENGTH, TYME, CHARGE, TEMPERATURE],
W:LISTIFY(W),
FOR U IN W DO (
V:RHS(U), U:LHS(U),
ACTUAL: LISTOFVARS(V),
FOR AC IN ACTUAL DO IF NOT MEMBER(AC,VALID) THEN PRINT(
"WARNING:", AC, "NOT MEMBER OF", VALID),
PUT(U,V,'DIMENSION))) $
LISTIFY(W) := IF LISTP(W) THEN W ELSE [W] $
%PURE: '[BOLTZMANNSCONSTANT, ELECTRICPERMITTIVITYOFAVACUUM] $
NONDIMENSIONALIZE(U) := BLOCK(/* U is a list of indeterminates
representing classes of physical quantities such as VELOCITY or
LENGTH, for which dimensions have previously been established
by the DIMENSION function. Returns a list of nondimensional
combinations of the physical quantities in U. */
/* ratmx:false in DOE MACSYMA */
[B, C, V, W, M, N, I, R, BASIS, LOGEXPAND, RATMX:false, SCALARMATRIXP],
U: LISTIFY(U),
/* Determine basis: */
M:N:0,
BASIS:[LENGTH, TYME, MASS, TEMPERATURE, CHARGE],
IF MEMBER('BOLTZMANNSCONSTANT, %PURE) THEN (M:M+1,
BASIS:DELETE('TEMPERATURE,BASIS)),
IF MEMBER('ELECTRICPERMITTIVITYOFAVACUUM,%PURE) THEN (M:M+1,
BASIS:DELETE('CHARGE,BASIS)),
IF MEMBER('GRAVITYCONSTANT,%PURE) THEN (N:N+1,
BASIS:DELETE('MASS,BASIS)),
IF MEMBER('PLANCKSCONSTANT,%PURE) THEN (N:N+1,
BASIS:DELETE('TYME,BASIS)),
IF MEMBER('SPEEDOFLIGHT,%PURE) THEN (N:N+1,
BASIS:DELETE('LENGTH,BASIS)),
IF BASIS=[] THEN RETURN(U),
IF N>0 AND M<2 THEN ERROR("INVALID TO INCLUDE GRAVITYCONSTANT",
"PLANCKSCONSTANT OR SPEEDOFLIGHT WITHOUT ALSO INCLUDING",
"BOLTZMANNSCONSTANT & ELECTRICPERMITTIVITYOFAVACUUM"),
C:B:V:W: [],
/* ratmx:false in DOE MACSYMA */
LOGEXPAND:/* RATMX: */TRUE, SCALARMATRIXP:FALSE,
N:0, M:LENGTH(BASIS),
/* Construct matrix of exponents: */
FOR UU IN U DO (B: GET(UU, 'DIMENSION),
IF B=FALSE THEN ERROR("FIRST DO AN APPROPRIATE DIMENSION(",''UU,
"= TERM WITH POWERS OF MASS, LENGTH, TYME, TEMPERATURE & CHARGE"
),
IF MEMBER('BOLTZMANNSCONSTANT, %PURE) THEN
B: SUBST(TEMPERATURE=MASS*LENGTH^2/TYME^2, B),
IF MEMBER(ELECTRICPERMITTIVITYOFAVACUUM,%PURE) THEN
B: SUBST(CHARGE=LENGTH^(3/2)*MASS^(1/2)/TYME, B),
IF MEMBER(SPEEDOFLIGHT,%PURE) THEN
IF MEMBER(PLANCKSCONSTANT,%PURE) THEN
B: SUBST([LENGTH=1/MASS,TYME=1/MASS], B)
ELSE IF MEMBER(GRAVITYCONSTANT,%PURE) THEN
B: SUBST([MASS=TYME,LENGTH=TYME], B)
ELSE B: SUBST(LENGTH=TYME, B)
ELSE IF MEMBER(PLANCKSCONSTANT,%PURE) THEN
IF MEMBER(GRAVITYCONSTANT,%PURE) THEN
B: SUBST([MASS=LENGTH^(-1/3), TYME=LENGTH^(-5/3)], B)
ELSE B: SUBST(TYME=MASS*LENGTH^2, B)
ELSE IF MEMBER(GRAVITYCONSTANT,%PURE) THEN
B: SUBST(MASS=LENGTH^3/TYME^2, B),
B:LOG(B), R:[],
FOR UU IN BASIS DO R:CONS(COEFF(B,LOG(UU)), R),
C:CONS(R,C), W:CONS(UU,W), N:N+1),
C:SUBSTINPART('MATRIX,C,0),
R:RANK(C),
IF R=0 THEN RETURN(U),
IF R=N THEN RETURN([]),
/* Delete dependent columns: */
I:1,
WHILE R<M DO (B:SUBMATRIX(C,I),
WHILE RANK(B)<R DO (I:I+1,
B:SUBMATRIX(C,I)),
M:M-1,
C:B),
/* Partition into a nonsingular part and the other rows: */
C:SUBSTINPART("[",C,0), B:[],
FOR J:1 THRU R DO(
B:CONS(FIRST(C),B),
WHILE RANK(SUBSTINPART('MATRIX,B,0))<J DO(
C:ENDCONS(FIRST(C),REST(C)),
B:CONS(FIRST(C),REST(B)),
W:ENDCONS(FIRST(W),REST(W))),
C:REST(C), V:CONS(FIRST(W),V), W:REST(W)),
C:SUBSTINPART('MATRIX,C,0), B:SUBSTINPART('MATRIX,B,0),
/* Form the matrix of physical-quantity exponents and the
corresponding dimensionless products: */
C: C.B^^-1, B:[],
FOR L:1 THRU N-R DO
B: CONS(W[L]/PRODUCT(V[K]^C[L,K],K,1,R), B),
RETURN(B)) $
DIMENSION([
ACCELERATION = LENGTH/TYME^2,
ANGLE = 1,
ANGULARACCELERATION = 1/TYME^2,
ANGULARMOMENTUM = MASS*LENGTH^2/TYME^2,
ANGULARVELOCITY = 1/TYME,
AREA = LENGTH^2,
BOLTZMANNSCONSTANT = MASS*LENGTH^2/TYME^2/TEMPERATURE,
CAPACITANCE = TYME^2*CHARGE^2/MASS/LENGTH^2,
CHARGE = CHARGE,
CURRENT = CHARGE/TYME,
CURRENTDENSITY = CHARGE/TYME/LENGTH^2,
DENSITY = MASS/LENGTH^3,
DISTANCE = LENGTH,
ELECTRICFIELD = MASS*LENGTH/TYME^2/CHARGE,
ELECTRICPERMITTIVITY = TYME^2*CHARGE^2/MASS/LENGTH^3,
ELECTRICPERMITTIVITYOFAVACUUM = TYME^2*CHARGE^2/MASS/LENGTH^3,
ENERGY = MASS*LENGTH^2/TYME^2,
ENTHALPY = LENGTH^2/TYME^2,
FREQUENCY = 1/TYME,
FILMCOEFFICIENT = MASS/TYME^3/TEMPERATURE,
FLOW = LENGTH^3/TYME,
GRAVITYCONSTANT = LENGTH^3/MASS/TYME^2,
HEAT = MASS*LENGTH^2/TYME^2,
HEATCAPACITY = MASS*LENGTH^2/TYME^2/TEMPERATURE,
HEATTRANSFERCOEFFICIENT = 1/TYME,
INDUCTANCE = MASS*LENGTH^2/CHARGE^2,
INTERNALENERGY = LENGTH^2/TYME^2,
KINEMATICVISCOSITY = LENGTH^2/TYME,
LENGTH = LENGTH,
MASS = MASS,
MOMENT = MASS*LENGTH^2/TYME^2,
MOMENTUM = MASS*LENGTH/TYME,
MAGNETICINDUCTION = MASS/TYME/CHARGE,
MAGNETICPERMITTIVITY = MASS*LENGTH/CHARGE^2,
PLANCKSCONSTANT = MASS*LENGTH^2/TYME,
POISSONSRATIO = 1,
POWER = MASS*LENGTH^2/TYME^3,
PRESSURE = MASS/LENGTH/TYME^2,
RESISTANCE = MASS*LENGTH^2/TYME/CHARGE^2,
SPECIFICHEAT = LENGTH^2/TYME^2/TEMPERATURE,
SPEEDOFLIGHT = LENGTH/TYME,
SHEARMODULUS = MASS/LENGTH/TYME^2,
SURFACETENSION = MASS/TYME^2,
STEFANBOLTZMANNCONSTANT = MASS/TYME^3/TEMPERATURE^4,
STRESS = MASS/LENGTH/TYME^2,
STRAIN = 1,
TEMPERATURE = TEMPERATURE,
THERMALCONDUCTIVITY = MASS*LENGTH/TYME^3/TEMPERATURE,
THERMALEXPANSIONCOEFFICIENT = 1/TEMPERATURE,
THERMALDIFFUSIVITY = LENGTH^2/TYME,
TYME = TYME,
VELOCITY = LENGTH/TYME,
VOLUME = LENGTH^3,
VOLTAGE = MASS*LENGTH^2/TYME^2/CHARGE,
VISCOSITY = MASS/TYME/LENGTH,
WORK = MASS*LENGTH^2/TYME^2,
YOUNGSMODULUS = MASS/LENGTH/TYME^2]) $
ALIAS(TIME,TYME,CPUTIME,TIME)$
TTYOFF: FALSE$
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