a9289f04-e224-409d-b53f-cc0092b6a979 18 15 12 decimal

&[DATE] &[TIME] - &[FILENAME]

h 100 : j 04 h 1 -^range : 21 sys

# Floor

floor/ceil codes ... applications

floor code, Andrey007 [20200408 x floor x 0 round x < x 0 round x 0 round 1 - if :

j B j h 1 -^+ Floor : j b j h 1 -^+ floor : 21 sys

evaluate j B vectorize j b vectorize 12 mat

j h 1 -^+ floor j h 1 -^+ Floor ≡

Stand alone section ... export =======================

Implicit 'zoom fractional' Up/Down Ω a b zoom a b ≡ (a b | (1 ≠ (& (=> ≡ => implicit conditions ≡ i 1 Ω rows a * (range j 1 Ω cols b * (range Nu i j el Ω i a / Ceil j b / Ceil el : a 1 ≥ Nu i j el Ω i a / Floor j b / Floor el : cases for for Nu 41 line :

rows

cols

M 2050255 Random.N : iMage M 1010 zoom : 21 sys

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 iMage

M 682001621283311952524413898982501992262721915322661452422481501589921121414315611421612061702206933201113812322422448039218325322312416224385176812081225424075237109144126551924329521418620711318116904701189627216175321045576308812202235217371001229811725205 mat

M nc nr Pad A M : i 1 A rows range j 1 nc range vert i j el 0 : for for a A 1 A rows 1 A cols 2 / Floor submatrix : b A 1 A rows A cols 2 / Floor 1 + A cols submatrix : S a vert b augment transpose : i 1 S rows range j 1 nr range horiz i j el 0 : for for a S 1 S rows 1 S cols 2 / Floor submatrix : b S 1 S rows S cols 2 / Floor 1 + S cols submatrix : S a horiz b augment transpose : 111 line :

L H N X N intervals U 0 : dx H L - N / : i 1 N 1 + (range U i el L dx i * dx - (+ : for U 51 line :

L 1 - : H 1 : N 51 : 13 mat

U L H N X :

V U :

Generate the symmetric square matrix x y f U V Sym r 1 : i 1 U rows range c 1 : j 1 V rows range M r c el U i el V j el f eval : c c 1 + : 21 line for r r 1 + : 31 line for M 31 line :

x y f 255 x 2^y 2^+ (- 0.5 / exp * :

pie x y f U V Sym 36 Pad :

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

black portion + for Fido the dog. Dogs love apple pie !

pie

h 100 : j 04 h 1 -^range : 21 sys

# Ceil

# Floor

n j rows : 401

ceil code ... opposite 'floor' x ceil x 0 round x > x 0 round x 0 round 1 + if :

n 1 j rows range :

j B j h 1 -^+ Floor : j b j h 1 -^+ floor : 21 sys

j a j h 1 -^+ Ceil : j c j h 1 -^+ ceil : 21 sys

n j B vectorize augment n j a vectorize augment 2 1 sys

M n 6 : m 2 : 12 mat i 1 n range j 1 n range M i j el i j + m mod : for for M 31 line :

M 01010110101001010110101001010110101066 mat

gray level N M 235 * :

Pixelation by  'zoom fractional' Up/Down M a b zoomfract a b ≡ (a b | (1 ≠ (& (implicit conditions ≡ i 1 M rows a * (range j 1 M cols b * (range N i j el M i a / Ceil j b / Ceil el : a 1 ≥ N i j el M i a / Floor j b / Floor el : cases for for N 31 line :

t0 1 time :

zoom N 1010 zoomfract :

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 zoom

1 time t0 - 3.2 s *