[Gridflow-cvs] [svn] commit: r5906 - in /trunk/doc: moulinette.tcl numop.pd

svn-gridflow at artengine.ca svn-gridflow at artengine.ca
Mon Aug 2 20:43:16 EDT 2010


Author: matju
Date: Mon Aug  2 20:43:16 2010
New Revision: 5906

Log:
...

Modified:
    trunk/doc/moulinette.tcl
    trunk/doc/numop.pd

Modified: trunk/doc/moulinette.tcl
==============================================================================
--- trunk/doc/moulinette.tcl (original)
+++ trunk/doc/moulinette.tcl Mon Aug  2 20:43:16 2010
@@ -46,9 +46,9 @@
 	lappend ::msgboxes $::oid
 	set x 10
 	foreach op1 $op {msg $x $y op $op; incr 50}
-	text                     $::col1 [expr {$y-4}] $desc
-	if {$extra1 != ""} {text $::col2 [expr {$y-4}] $extra1}
-	if {$extra2 != ""} {text $::col3 [expr {$y-4}] $extra2}
+	text                     $::col1 $y $desc
+	if {$extra1 != ""} {text $::col2 $y $extra1}
+	if {$extra2 != ""} {text $::col3 $y $extra2}
 	incr ::row
 	incr ::y $size
 }
@@ -162,9 +162,14 @@
 p {
 	note: a centidegree is 0.01 degree. There are 36000 centidegrees in a circle.
         Some angle operators use centidegrees, while some others use radians. To
-        convert degrees into centidegrees, multiply by 100.
+        convert degrees into centidegrees, multiply by 100 .
         To convert degrees into radians, divide by 57.2957 .
         Thus, to convert centidegrees into radians, divide by 5729.57 .
+        All the complex number operators are only for floats.
+	VecOps are called VecOps because each operation happens between more than just two numbers.
+	Complex VecOps are those that arise when a pair of numbers (A0 A1) is considered as a single number A0+A1*sqrt(-1).
+	If you need complex numbers but don't know yet how they work,
+	learn them using a math tutorial and then those VecOps will begin to look familiar.
 }
 
 close $fh

Modified: trunk/doc/numop.pd
==============================================================================
--- trunk/doc/numop.pd (original)
+++ trunk/doc/numop.pd Mon Aug  2 20:43:16 2010
@@ -7,258 +7,258 @@
 #X text 676 30 effect on coords;
 #X obj 0 70 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 70 op ignore;
-#X text 96 66  A ;
-#X text 446 66 no effect;
-#X text 676 66 no effect;
+#X text 96 70  A ;
+#X text 446 70 no effect;
+#X text 676 70 no effect;
 #X obj 0 89 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 89 op put;
-#X text 96 85  B ;
-#X text 446 85 replace by;
-#X text 676 85 replace by;
+#X text 96 89  B ;
+#X text 446 89 replace by;
+#X text 676 89 replace by;
 #X obj 0 108 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 108 op +;
-#X text 96 104  A + B ;
-#X text 446 104 brightness \,  crossfade;
-#X text 676 104 move \,  morph;
+#X text 96 108  A + B ;
+#X text 446 108 brightness \,  crossfade;
+#X text 676 108 move \,  morph;
 #X obj 0 127 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 127 op -;
-#X text 96 123  A - B ;
-#X text 446 123 brightness \,  motion detection;
-#X text 676 123 move \,  motion detection;
+#X text 96 127  A - B ;
+#X text 446 127 brightness \,  motion detection;
+#X text 676 127 move \,  motion detection;
 #X obj 0 146 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 146 op inv+;
-#X text 96 142  B - A ;
-#X text 446 142 negate then contrast;
-#X text 676 142 180 degree rotate then move;
+#X text 96 146  B - A ;
+#X text 446 146 negate then contrast;
+#X text 676 146 180 degree rotate then move;
 #X obj 0 165 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 165 op *;
-#X text 96 161  A * B ;
-#X text 446 161 contrast;
-#X text 676 161 zoom out;
+#X text 96 165  A * B ;
+#X text 446 165 contrast;
+#X text 676 165 zoom out;
 #X obj 0 184 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 184 op *>>8;
-#X text 96 180  (A * B) >> 8 ;
-#X text 446 180 contrast;
-#X text 676 180 zoom out;
+#X text 96 184  (A * B) >> 8 ;
+#X text 446 184 contrast;
+#X text 676 184 zoom out;
 #X obj 0 203 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 203 op /;
-#X text 96 199  A / B \,  rounded towards zero ;
-#X text 446 199 contrast;
-#X text 676 199 zoom in;
+#X text 96 203  A / B \,  rounded towards zero ;
+#X text 446 203 contrast;
+#X text 676 203 zoom in;
 #X obj 0 222 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 222 op div;
-#X text 96 218  A / B \,  rounded downwards ;
-#X text 446 218 contrast;
-#X text 676 218 zoom in;
+#X text 96 222  A / B \,  rounded downwards ;
+#X text 446 222 contrast;
+#X text 676 222 zoom in;
 #X obj 0 241 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 241 op inv*;
-#X text 96 237  B / A \,  rounded towards zero ;
+#X text 96 241  B / A \,  rounded towards zero ;
 #X obj 0 260 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 260 op swapdiv;
-#X text 96 256  B / A \,  rounded downwards ;
+#X text 96 260  B / A \,  rounded downwards ;
 #X obj 0 279 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 279 op %;
-#X text 96 275  A % B \,  modulo (goes with div) ;
-#X text 446 275 --;
-#X text 676 275 tile;
+#X text 96 279  A % B \,  modulo (goes with div) ;
+#X text 446 279 --;
+#X text 676 279 tile;
 #X obj 0 298 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 298 op swap%;
-#X text 96 294  B % A \,  modulo (goes with div) ;
+#X text 96 298  B % A \,  modulo (goes with div) ;
 #X obj 0 317 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 317 op rem;
-#X text 96 313  A % B \,  remainder (goes with /) ;
+#X text 96 317  A % B \,  remainder (goes with /) ;
 #X obj 0 336 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 336 op swaprem;
-#X text 96 332  B % A \,  remainder (goes with /) ;
+#X text 96 336  B % A \,  remainder (goes with /) ;
 #X obj 0 355 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 355 op gcd;
-#X text 96 351 greatest common divisor;
+#X text 96 355 greatest common divisor;
 #X obj 0 374 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 374 op lcm;
-#X text 96 370 least common multiple;
+#X text 96 374 least common multiple;
 #X obj 0 393 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 393 op |;
-#X text 96 389  A or B \,  bitwise ;
-#X text 446 389 bright munchies;
-#X text 676 389 bottomright munchies;
+#X text 96 393  A or B \,  bitwise ;
+#X text 446 393 bright munchies;
+#X text 676 393 bottomright munchies;
 #X obj 0 412 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 412 op ^;
-#X text 96 408  A xor B \,  bitwise ;
-#X text 446 408 symmetric munchies (fractal checkers);
-#X text 676 408 symmetric munchies (fractal checkers);
+#X text 96 412  A xor B \,  bitwise ;
+#X text 446 412 symmetric munchies (fractal checkers);
+#X text 676 412 symmetric munchies (fractal checkers);
 #X obj 0 431 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 431 op &;
-#X text 96 427  A and B \,  bitwise ;
-#X text 446 427 dark munchies;
-#X text 676 427 topleft munchies;
+#X text 96 431  A and B \,  bitwise ;
+#X text 446 431 dark munchies;
+#X text 676 431 topleft munchies;
 #X obj 0 450 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 450 op <<;
-#X text 96 446  A * pow(2 \, mod(B \, 32)) \,  which is left-shifting ;
-#X text 446 446 like *;
-#X text 676 446 like *;
+#X text 96 450  A * pow(2 \, mod(B \, 32)) \,  which is left-shifting ;
+#X text 446 450 like *;
+#X text 676 450 like *;
 #X obj 0 469 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 469 op >>;
-#X text 96 465  A / pow(2 \, mod(B \, 32)) \,  which is right-shifting ;
-#X text 446 465 like / \, div;
-#X text 676 465 like / \, div;
+#X text 96 469  A / pow(2 \, mod(B \, 32)) \,  which is right-shifting ;
+#X text 446 469 like / \, div;
+#X text 676 469 like / \, div;
 #X obj 0 488 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 488 op ||;
-#X text 96 484  if A is zero then B else A ;
+#X text 96 488  if A is zero then B else A ;
 #X obj 0 507 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 507 op &&;
-#X text 96 503  if A is zero then zero else B;
+#X text 96 507  if A is zero then zero else B;
 #X obj 0 526 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 526 op min;
-#X text 96 522  the lowest value in A \, B ;
-#X text 446 522 clipping;
-#X text 676 522 clipping (of individual points);
+#X text 96 526  the lowest value in A \, B ;
+#X text 446 526 clipping;
+#X text 676 526 clipping (of individual points);
 #X obj 0 545 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 545 op max;
-#X text 96 541  the highest value in A \, B ;
-#X text 446 541 clipping;
-#X text 676 541 clipping (of individual points);
+#X text 96 545  the highest value in A \, B ;
+#X text 446 545 clipping;
+#X text 676 545 clipping (of individual points);
 #X obj 0 564 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 564 op cmp;
-#X text 96 560  -1 when A<B \,  0 when A=B \,  1 when A>B ;
+#X text 96 564  -1 when A<B \,  0 when A=B \,  1 when A>B ;
 #X obj 0 583 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 583 op ==;
-#X text 96 579  is A equal to B ? 1=true \,  0=false ;
+#X text 96 583  is A equal to B ? 1=true \,  0=false ;
 #X obj 0 602 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 602 op !=;
-#X text 96 598  is A not equal to B ? ;
+#X text 96 602  is A not equal to B ? ;
 #X obj 0 621 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 621 op >;
-#X text 96 617  is A greater than B ? ;
+#X text 96 621  is A greater than B ? ;
 #X obj 0 640 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 640 op <=;
-#X text 96 636  is A not greater than B ? ;
+#X text 96 640  is A not greater than B ? ;
 #X obj 0 659 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 659 op <;
-#X text 96 655  is A less than B ? ;
+#X text 96 659  is A less than B ? ;
 #X obj 0 678 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 678 op >=;
-#X text 96 674 is A not less than B ? ;
+#X text 96 678 is A not less than B ? ;
 #X obj 0 697 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 697 op sin*;
-#X text 96 693  B * sin(A) in centidegrees ;
-#X text 446 693 --;
-#X text 676 693 waves \,  rotations;
+#X text 96 697  B * sin(A) in centidegrees ;
+#X text 446 697 --;
+#X text 676 697 waves \,  rotations;
 #X obj 0 716 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 716 op cos*;
-#X text 96 712  B * cos(A) in centidegrees ;
-#X text 446 712 --;
-#X text 676 712 waves \,  rotations;
+#X text 96 716  B * cos(A) in centidegrees ;
+#X text 446 716 --;
+#X text 676 716 waves \,  rotations;
 #X obj 0 735 cnv 15 906 26 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 735 op atan;
-#X text 96 731  arctan(A/B) in centidegrees ;
-#X text 446 731 --;
-#X text 676 731 find angle to origin \;  (part of polar transform);
+#X text 96 735  arctan(A/B) in centidegrees ;
+#X text 446 735 --;
+#X text 676 735 find angle to origin \;  (part of polar transform);
 #X obj 0 763 cnv 15 906 26 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 763 op tanh*;
-#X text 96 759  B * tanh(A) in centidegrees ;
-#X text 446 759 smooth clipping;
-#X text 676 759 smooth clipping (of individual points) \;  neural sigmoid \,  fuzzy logic;
+#X text 96 763  B * tanh(A) in centidegrees ;
+#X text 446 763 smooth clipping;
+#X text 676 763 smooth clipping (of individual points) \;  neural sigmoid \,  fuzzy logic;
 #X obj 0 791 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 791 op log*;
-#X text 96 787  B * log(A) in base e ;
+#X text 96 791  B * log(A) in base e ;
 #X obj 0 810 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 810 op /exp;
-#X text 96 806  exp(A / B) in base e ;
+#X text 96 810  exp(A / B) in base e ;
 #X obj 0 829 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 829 op gamma;
-#X text 96 825  floor(pow(a/256.0 \, 256.0/b)*256.0) ;
-#X text 446 825 gamma correction;
+#X text 96 829  floor(pow(a/256.0 \, 256.0/b)*256.0) ;
+#X text 446 829 gamma correction;
 #X obj 0 848 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 848 op **;
-#X text 96 844  A**B \,  that is \,  A raised to power B ;
-#X text 446 844 gamma correction;
+#X text 96 848  A**B \,  that is \,  A raised to power B ;
+#X text 446 848 gamma correction;
 #X obj 0 867 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 867 op abs-;
-#X text 96 863  absolute value of (A-B) ;
+#X text 96 867  absolute value of (A-B) ;
 #X obj 0 886 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 886 op rand;
-#X text 96 882  randomly produces a non-negative number below A ;
+#X text 96 886  randomly produces a non-negative number below A ;
 #X obj 0 905 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 905 op sqrt;
-#X text 96 901  square root of A \,  rounded downwards ;
+#X text 96 905  square root of A \,  rounded downwards ;
 #X obj 0 924 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 924 op sq-;
-#X text 96 920  (A-B) times (A-B) ;
+#X text 96 924  (A-B) times (A-B) ;
 #X obj 0 943 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 943 op avg;
-#X text 96 939  (A+B)/2 ;
+#X text 96 943  (A+B)/2 ;
 #X obj 0 962 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 962 op hypot;
-#X text 96 958  distance function: square root of (A*A+B*B) ;
+#X text 96 962  distance function: square root of (A*A+B*B) ;
 #X obj 0 981 cnv 15 906 26 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 981 op clip+;
-#X text 96 977  like A+B but overflow causes clipping instead of wrapping around ;
+#X text 96 981  like A+B but overflow causes clipping instead of wrapping around ;
 #X obj 0 1009 cnv 15 906 26 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 1009 op clip-;
-#X text 96 1005  like A-B but overflow causes clipping instead of wrapping around ;
+#X text 96 1009  like A-B but overflow causes clipping instead of wrapping around ;
 #X obj 0 1037 cnv 15 906 26 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 1037 op erf*;
-#X text 96 1033  integral of e^(-x*x) dx ... (coming soon \;  what ought to be the scaling factor?) ;
+#X text 96 1037  integral of e^(-x*x) dx ... (coming soon \;  what ought to be the scaling factor?) ;
 #X obj 0 1065 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 1065 op weight;
-#X text 96 1061  number of "1" bits in an integer;
+#X text 96 1065  number of "1" bits in an integer;
 #X obj 0 1084 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 1084 op sin;
-#X text 96 1080 sin(A-B) in radians \,  float only;
+#X text 96 1084 sin(A-B) in radians \,  float only;
 #X obj 0 1103 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 1103 op cos;
-#X text 96 1099 cos(A-B) in radians \,  float only;
+#X text 96 1103 cos(A-B) in radians \,  float only;
 #X obj 0 1122 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 1122 op atan2;
-#X text 96 1118 atan2(A \, B) in radians \,  float only;
+#X text 96 1122 atan2(A \, B) in radians \,  float only;
 #X obj 0 1141 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 1141 op tanh;
-#X text 96 1137 tanh(A-B) in radians \,  float only;
+#X text 96 1141 tanh(A-B) in radians \,  float only;
 #X obj 0 1160 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 1160 op exp;
-#X text 96 1156 exp(A-B) in radians \,  float only;
+#X text 96 1160 exp(A-B) in radians \,  float only;
 #X obj 0 1179 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 1179 op log;
-#X text 96 1175 log(A-B) in radians \,  float only;
+#X text 96 1179 log(A-B) in radians \,  float only;
 #X obj 0 1214 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 1214 op C.*    ;
-#X text 96 1210 A*B;
+#X text 96 1214 A*B;
 #X obj 0 1233 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 1233 op C.*conj;
-#X text 96 1229 A*conj(B);
+#X text 96 1233 A*conj(B);
 #X obj 0 1252 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 1252 op C./    ;
-#X text 96 1248 A/B;
+#X text 96 1252 A/B;
 #X obj 0 1271 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 1271 op C./conj;
-#X text 96 1267 A/conj(B);
+#X text 96 1271 A/conj(B);
 #X obj 0 1290 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 1290 op C.sq-  ;
-#X text 96 1286 (A-B)*(A-B);
+#X text 96 1290 (A-B)*(A-B);
 #X obj 0 1309 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 1309 op C.abs- ;
-#X text 96 1305 abs(A-B);
+#X text 96 1309 abs(A-B);
 #X obj 0 1328 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 1328 op C.sin  ;
-#X text 96 1324 sin(A-B);
+#X text 96 1328 sin(A-B);
 #X obj 0 1347 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 1347 op C.cos  ;
-#X text 96 1343 cos(A-B);
+#X text 96 1347 cos(A-B);
 #X obj 0 1366 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 1366 op C.tanh ;
-#X text 96 1362 tanh(A-B);
+#X text 96 1366 tanh(A-B);
 #X obj 0 1385 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 1385 op C.exp  ;
-#X text 96 1381 exp(A-B);
+#X text 96 1385 exp(A-B);
 #X obj 0 1404 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 1404 op C.log  ;
-#X text 96 1400 log(A-B);
+#X text 96 1404 log(A-B);
 #X obj 0 1439 cnv 15 906 17 empty empty empty 20 12 0 14 -249792 -66577 0;
 #X msg 10 1439 op c2p;
-#X text 96 1435 hypot \, atan two-in-one;
+#X text 96 1439 hypot \, atan two-in-one;
 #X obj 0 1458 cnv 15 906 17 empty empty empty 20 12 0 14 -233280 -66577 0;
 #X msg 10 1458 op p2c;
-#X text 96 1454 cos* \, sin* two-in-one;
+#X text 96 1458 cos* \, sin* two-in-one;
 #X obj 10 1487 outlet;
 #X connect 7 0 260 0;
 #X connect 12 0 260 0;
@@ -342,7 +342,12 @@
 #X text 10 1507 
 	note: a centidegree is 0.01 degree. There are 36000 centidegrees in a circle.
         Some angle operators use centidegrees \,  while some others use radians. To
-        convert degrees into centidegrees \,  multiply by 100.
+        convert degrees into centidegrees \,  multiply by 100 .
         To convert degrees into radians \,  divide by 57.2957 .
         Thus \,  to convert centidegrees into radians \,  divide by 5729.57 .
+        All the complex number operators are only for floats.
+	VecOps are called VecOps because each operation happens between more than just two numbers.
+	Complex VecOps are those that arise when a pair of numbers (A0 A1) is considered as a single number A0+A1*sqrt(-1).
+	If you need complex numbers but don't know yet how they work \, 
+	learn them using a math tutorial and then those VecOps will begin to look familiar.
 ;



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