User:Tom Allen/ta/AddendumX07P01

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... check tensor for lowering indices on tensors (x-coordinates) ...


NB. ... execute (ijx) ...

   xCpts=:_ 0.9 2 26,_ 0.1p1 0.9p1 26,_ 0.1p1 1.8p1 26,:_ 0 2p1 26"_

   qR0A=:(''([mcvdc       xRef@([hkyX07A zfyc"_ 1))])                                ((0,50"_)pTRandom xCpts)''
   qR0B=:(''(0|:])@([:(''([(0{])@mcv       xRef@([hkyX07A zfyc"_ 1)),:@])D.1])"_ 1]) ((0,50"_)pTRandom xCpts)''

   qR0A (((2^_25);2^_20)qteq[;])"3 qR0B
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

   qR0A=:(''([mcvdcdc     xRef@([hkyX07A zfyc"_ 1))])                                ((0,50"_)pTRandom xCpts)''
   qR0B=:(''(0|:])@([:(''([(0{])@mcvdc     xRef@([hkyX07A zfyc"_ 1)),:@])D.1])"_ 1]) ((0,50"_)pTRandom xCpts)''

   qR0A (((2^_25);2^_16)qteq[;])"4 qR0B
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

   qR0A=:(''([mcvdcdcdc   xRef@([hkyX07A zfyc"_ 1))])                                ((0,50"_)pTRandom xCpts)''
   qR0B=:(''(0|:])@([:(''([(0{])@mcvdcdc   xRef@([hkyX07A zfyc"_ 1)),:@])D.1])"_ 1]) ((0,50"_)pTRandom xCpts)''

   qR0A (((2^_25);2^_16)qteq[;])"5 qR0B
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

   qR0A=:(''([mcvdcdcdcdc xRef@([hkyX07A zfyc"_ 1))])                                ((0,50"_)pTRandom xCpts)''
   qR0B=:(''(0|:])@([:(''([(0{])@mcvdcdcdc xRef@([hkyX07A zfyc"_ 1)),:@])D.1])"_ 1]) ((0,50"_)pTRandom xCpts)''

   qR0A (((2^_23);2^_16)qteq[;])"6 qR0B
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


... check tensor for raising indices on tensors (x-coordinates) ...


NB. ... execute (ijx) ...

   xCpts=:_ 0.9 2 26,_ 0.1p1 0.9p1 26,_ 0.1p1 1.8p1 26,:_ 0 2p1 26"_

   qR0A=:(''([mcndc       xRef@([hkyX07A zfyc"_ 1))])                                ((0,50"_)pTRandom xCpts)''
   qR0B=:(''(0|:])@([:(''([(0{])@mcn       xRef@([hkyX07A zfyc"_ 1)),:@])D.1])"_ 1]) ((0,50"_)pTRandom xCpts)''

   qR0A (((2^_25);2^_19)qteq[;])"3 qR0B
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

   qR0A=:(''([mcndcdc     xRef@([hkyX07A zfyc"_ 1))])                                ((0,50"_)pTRandom xCpts)''
   qR0B=:(''(0|:])@([:(''([(0{])@mcndc     xRef@([hkyX07A zfyc"_ 1)),:@])D.1])"_ 1]) ((0,50"_)pTRandom xCpts)''

   qR0A (((2^_22);2^_19)qteq[;])"4 qR0B
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

   qR0A=:(''([mcndcdcdc   xRef@([hkyX07A zfyc"_ 1))])                                ((0,50"_)pTRandom xCpts)''
   qR0B=:(''(0|:])@([:(''([(0{])@mcndcdc   xRef@([hkyX07A zfyc"_ 1)),:@])D.1])"_ 1]) ((0,50"_)pTRandom xCpts)''

   qR0A (((2^_18);2^_18)qteq[;])"5 qR0B
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


... check Christoffel symbols of the second kind (x-coordinates) ...


NB. ... execute (ijx) ...

   xCpts=:_ 0.9 2 26,_ 0.1p1 0.9p1 26,_ 0.1p1 1.8p1 26,:_ 0 2p1 26"_

   qR0A=:(''([ch2kdc       xRef@([hkyX07A zfyc"_ 1))])                                ((0,50"_)pTRandom xCpts)''
   qR0B=:(''(0|:])@([:(''([(0{])@ch2k       xRef@([hkyX07A zfyc"_ 1)),:@])D.1])"_ 1]) ((0,50"_)pTRandom xCpts)''

   qR0A (((2^_26);2^_16)qteq[;])"4 qR0B
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

   qR0A=:(''([ch2kdcdc     xRef@([hkyX07A zfyc"_ 1))])                                ((0,50"_)pTRandom xCpts)''
   qR0B=:(''(0|:])@([:(''([(0{])@ch2kdc     xRef@([hkyX07A zfyc"_ 1)),:@])D.1])"_ 1]) ((0,50"_)pTRandom xCpts)''

   qR0A (((2^_23);2^_16)qteq[;])"5 qR0B
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

   qR0A=:(''([ch2kdcdcdc   xRef@([hkyX07A zfyc"_ 1))])                                ((0,50"_)pTRandom xCpts)''
   qR0B=:(''(0|:])@([:(''([(0{])@ch2kdcdc   xRef@([hkyX07A zfyc"_ 1)),:@])D.1])"_ 1]) ((0,50"_)pTRandom xCpts)''

   qR0A (((2^_19);2^_16)qteq[;])"6 qR0B
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1



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