wedge.R
In stokes: The Exterior Calculus

## ----setup, include=FALSE-----------------------------------------------------
knitr::opts_chunk$set(echo = TRUE)
library("stokes")
library("spray")  # needed for spraycross()
set.seed(0)

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wedge
wedge2

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(a <- spray(matrix(1:4,2,2),c(2,5)))
(b <- spray(matrix(c(10,11,12,13),2,2),c(7,11)))
spraycross(a,b)
spraycross(b,a)

## -----------------------------------------------------------------------------
(x <- as.kform(cbind(1,2),5))
(y <- as.kform(cbind(3,4,7),7))
wedge2(x,y)

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 tx <- as.ktensor(x)    # "tx" = tensor 'x'
(ty <- as.ktensor(y))   # "ty" = tensor 'y'

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M <- matrix(round(rnorm(21),2),7,3) # member of (R^7)^3
c(as.function(y)(M),as.function(ty)(M))

## -----------------------------------------------------------------------------
7*(
 +M[3,1]*M[4,2]*M[7,3] 
 -M[3,1]*M[4,3]*M[7,2] 
 -M[3,2]*M[4,1]*M[7,3] 
 +M[3,2]*M[4,3]*M[7,1] 
 +M[3,3]*M[4,1]*M[7,2]
 -M[3,3]*M[4,2]*M[7,1]
 )

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(z <- tensorprod(as.ktensor(x),as.ktensor(y)))

## -----------------------------------------------------------------------------
wedge(x,y)

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(omega <- as.kform(rbind(c(1,2,8),c(1,3,7)),5:6))

## -----------------------------------------------------------------------------
eta <- as.kform(rbind(c(2,3,5),c(3,5,6)),2:3)
wedge(omega,eta)