Information: A function is an equation that, when a number is input, gives one (and only one) output. Functions include: Linear formula, Quadratic formula, Cubic formula, Quartic formula, Modulo, Logarithm, Simple roots, Factors, Prime factors, Percents, Primality, Totient (phi), Gamma (N!), Averages, Arith. mean, Harmonic mean, Median, Range, Std. deviation, Variance, Percents, trig functions. Functions are an integral part of mathematics and many sciences, including computer science.
 
        Outline: Algebra functions
Instructions: Click on the instruction (in blue) to go to that portion of the program
Outline:
  Line 0. Clear
  Line 3 - 13. Menu
  Line 16 - 20. Linear formula
  Line 21 - 25. Quadratic formula
  Line 26 - 53. Cubic formula
  Line 54 - 111. Quartic formula
  Line 112 - 116. Modulo
  Line 117 - 121. Logarithm
  Line 122 - 136. Simple roots
  Line 137 - 151. Factors
  Line 152 - 154. Prime factors
  Line 155 - 173. Percents
  Line 174 - 190. Primality
  Line 191 - 201. Totient (phi)
  Line 202 - 213. Gamma (N!)
  Line 214 - 216. Averages
  Line 217 - 219. Arith. mean
  Line 220 - 222. Geometric mean
  Line 223 - 222. Harmonic mean
  Line 223 - 225. Median
  Line 226 - 228. Range
  Line 229 - 232. Std. deviation
  Line 233 - 235. Variance
  Line 236 - 239. Percents
  Line 240 - 244. sec/csc/cot
  Line 245 - 247. Menu trig functions
  Line 236 - 239. Percents
 
 
  Line 250 - 252. sec(
  Line 253 - 255. csc(
  Line 256 - 258. cot(
  Line 259 - 261. sec‾¹
  Line 262 - 267. cot‾¹(
  Line 268 - 270. sech(
  Line 271 - 273. csch(
  Line 274 - 276. coth(
  Line 277 - 280. sech‾¹(
  Line 281 - 283. csch‾¹(
  Line 284 - 286. coth‾¹
  Line 287 - 290. Filter (sinc)
  Line 291 - 294. Euler (cis)
  Line 295 - 301. Sequences
  Line 302 - 309. Summation
  Line 310 - 317. Product
  Line 318 - 328. Limits
  Line 329 - 336. Pascal's
  Line 337 - 345. Fibonacci
  Line 346 - 265. Phi ()
  Line 349 - 365. Base converter
  Line 366 - 373. Dice
  Line 374 - 378. Digit count
  Line 379 - 383. Sign
  Line 384 - 406. Bitwise logic
    Examples
    Screenshots
    Reference
    Reference Links
 
1. Float:a+bi
2. Lbl θ1
3. Menu("FORMULA","Linear",1,"Quadratic",2,"Cubic",3,"Quartic",4,"Modulo",5,"Logarithm",6,"More...",θ2
4. Lbl θ2
5. Menu("FORMULA","Back...",θ1,"Simple roots",7,"Factors",8,"Prime factors",9,"Primality",A,"Totient (phi)",B,"More...",θ3
6. Lbl θ3
7. Menu("FORMULA","Back...",θ2,"Gamma (N!)",C,"Averages",D,"Percents",E,"sec/csc/cot",F,"Filter (sinc)",G,"More...",θ4
8. Lbl θ4
9. Menu("FORMULA","Back...",θ3,"Euler (cis)",H,"Sequences",I,"Summation",J,"Product",K,"Limits",L,"More...",θ5
10. Lbl θ5
11. Menu("FORMULA","Back...",θ4,"Pascal's ",M,"Fibonacci",N,"Phi ()",O,"Base converter",P,"Dice",Q,"More...",θ6
12. Lbl θ6
13. Menu("FORMULA","Back...",θ5,"Digit count",R,"Sign",S,"Bitwise logic",T,"Quit...",0
14. Lbl 0
15. Return
16.
Lbl 1           Linear formula
17. Prompt A,B
18. B/A->θ
19. DelVar ADelVar B
20. Goto θV
21.
Lbl 2           Quadratic formula
22. Prompt A,B,C
23. ({1,¯1}√(B²-4AC)-B)/(2A->L2
24. DelVar ADelVar BDelVar C
25. Goto θL
26.
Lbl 3           Cubic formula
27. Prompt A,B,C,D
28. ((3C/A)-(B/A)²)/3->F
29. ((2B³/A³)-(9BC/A²)+(27D/A))/27->G
30. (G²/4)+(F³/27->H
31. If H>0:Then
32. ¯(G/2)+√(H->R
33. ³√(R->S
34. ¯(G/2)-√(H->T
35. ³√(T->U
36. (S+U)-B/(3A->X
37. -(S+U)/2-B/(3A)+i(S-U)√(3)/2->Y
38. -(S+U)/2-B/(3A)-i(S-U)√(3)/2->Z
39. Else
40. √((G^2/4)-H->I
41. ³√(I->J
42. cos-¹( ¯G/(2I->K
43. ¯ J->L
44. cos(K/3->M
45. √(3)sin(K/3->N
46. ¯ B/(3A->P
47. 2JM+P->X
48. L(M+N)+P->Y
49. L(M-N)+P->Z
50. End
51. {X,Y,Z->L2
52. DelVar ADelVar BDelVar CDelVar DDelVar FDelVar GDelVar HDelVar RDelVar SDelVar TDelVar UDelVar XDelVar YDelVar ZDelVar IDelVar JDelVar KDelVar LDelVar MDelVar NDelVar P
53. Goto θL
54.
Lbl 4           Quartic formula
55. Prompt A,B,C,D,E
56. (8AC-3B²)/(8A²->F
57. (2B³-8ABC+16A²D)/(16A³->G
58. ( ¯ 3B&sup4;+16AB^2C-64A²BD+256A³E)/(256A&sup4;->H
59. 2F->U
60. F²-4H->V
61. ¯ G²->W
62. ( ¯ 2U³+9UV-27W)/54->I
63. ((3V-U²)/9)³->J
64. B/(4A->O
65. I²+J->L
66. U/3->K
67. If L<0:Then
68. √(³√(I+i√( ¯ L))+^3√(I-i√(-L))-K->M
69. Else
70. √(³√(I+√(L))+³√(I-√(L))-K->M
71. End
72. real(M->M
73. If M=0:Then
74. ¯ F->L
75. U²-4V->N
76. If real(N)<0
77. Then
78. √(L-(i√( ¯ N))/(2A->M
79. If real(M)=0
80. Then
81. sqrt(L-(i√(-N))/(2A->M
82. End
83. Else
84. √(L+√(N)/(2A->M
85. If real(M)=0
86. Then
87. √(L-√(N)/(2A->M
88. End:End:End
89. M²-2(F+M²-(G/M->N
90. ( ¯ M/2)-O->P
91. If real(N)<0
92. Then
93. P+(i√( ¯ N))/2->Q
94. P-(i√( ¯ N))/2->R
95. Else
96. P+√(N)/2->Q
97. P-√(N)/2->R
98. End
99. M²-2(F+M²+(G/M->N
100. (M/2)-O->P
101. If real(N)<0 102. Then
103. P+i√( ¯ N)/2->S
104. P-i√( ¯ N)/2->T
105. Else
106. P+√(N)/2->S
107. P-√(N)/2->T
108. End
109. {Q,R,S,T->L2
110. DelVar ADelVar BDelVar CDelVar DDelVar EDelVar FDelVar GDelVar HDelVar UDelVar VDelVar WDelVar IDelVar JDelVar ODelVar LDelVar KDelVar MDelVar NDelVar PDelVar QDelVar RDelVar SDelVar T
111. Goto θL
112.
Lbl 5           Modulo
113. Prompt A,B
114. A-Bint(A/B->θ
115. DelVar ADelVar B
116. Goto θV
117.
Lbl 6           Logarithm
118. Prompt N,B
119. log(N)/log(B->θ
120. DelVar NDelVar B
121. Goto θV
122.
Lbl 7           Simple roots
123. Prompt N
124. N->M:1->C
125. int(√(M->R
126. While R1
127. M/R²->D
128. If D=int(D
129. Then
130. D->M:CR->C
131. End
132. R-1->R
133. End
134. {C,M->L2
135. DelVar NDelVar MDelVar CDelVar RDelVar D
136. Goto θL
137.
Lbl 8           Factors
138. Prompt N
139. abs(N->M
140. If M=0 or M=1:Then
141. {M->L2
142. DelVar NDelVar M
143. Goto θL
144. End
145. {1,M->L2
146. For(F,2,√(M
147. If fPart(M/F)=0
148. augment(L2,{F,M/F->L2
149. End
150. DelVar NDelVar MDelVar F
151. Goto θL
152.
Lbl 9           Prime factors
153. Prompt N
154. N->M:2->S:{1->L2
155. Lbl 91
156. √(M->R
157. For(F,S,R
158. M/F->Q
159. If Q=int(Q
160. Then
161. augment(L2,{F->L2
162. Q->M:F->S
163. Goto 91
164. End
165. If F2:F+1->F
166. End
167. augment(L2,{M->L2
168. For(S,2,dim(L2
169. L2(S->L2(S-1
170. End
171. dim(L2)-1->dim(L2
172. DelVar NDelVar MDelVar SDelVar RDelVar FDelVar Q
173. Goto θL
174.
Lbl A           Primality
175. Prompt N
176. abs(N->M
177. DelVar θ
178. If M=1 or M=0
179. Then
180. DelVar NDelVar MDelVar D
181. Goto θV
182. End
183. For(D,2,√(M
184. If not(fPart(M/D:Then
185. DelVar NDelVar MDelVar D
186. Goto θV
187. End:End
188. 1->θ
189. DelVar NDelVar MDelVar D
190. Goto θV
191.
Lbl C           Totient (phi)
192. Prompt N
193. 2->θ
194. For(I,2,(N/2
195. If gcd(N,I)=1
196. 2+θ->θ
197. End
198. If N=1 or N=2
199. 1->θ
200. DelVar NDelVar SDelVar I
201. Goto θV
202.
Lbl C           Gamma (N!)
203. Prompt N
204. If int(N)=N
205. Then
206. abs(N)!->θ
207. If N<0
208. θ-2abs(N)!->θ
209. Else
210. fnInt(T^(N)^(T),T,0,2->θ
211. DelVar NDelVar T
212. End
213. Goto θV 214.
Lbl D           Averages
215. Prompt (L2
216. Menu("AVERAGE","Arith. mean",D1,"Geom. mean",D2,"Harmonic mean",D3,"Median",D4,"Range",D5,"Std. deviation",D6,"Variance",D7
217.
Lbl D1           Arith. mean
218. mean(L2->θ
219. Goto θV
220.
Lbl D2           Geom. mean
221. dim(L2)√(prod(L2->θ
222. Goto θV
223.
Lbl D3           Harmonic mean
224. dim(L2)/sum(L2->
225. Goto θV
226.
Lbl D4           Median
227. median(L2->θ
228. Goto θV
229.
Lbl D5           Range
230. SortD(L2
231. L2(1)-L2(dim(L2->θ
232. Goto θV
233.
Lbl D6           Std. deviation
234. stdDev(L2->θ
235. Goto θV
236.
Lbl D7           Variance
237. variance(L2->θ
238. Goto θV
239.
Lbl E           Percents
240. Prompt N,P
241. NP2->θ
242. DelVar NDelVar P
243. Goto θV
244.
Lbl F           sec/csc/cot
245. Prompt θ
246. Lbl F0
247.
Menu("FUNCTION","sec(",F1,"csc(",F2,"cot(",F3,"sec‾¹(",F4,"csc‾¹(",F5,"cot‾¹(",F6,"More...",F7
248. Lbl F7           More
249. Menu("FUNCTION","Back...",F0,"sech(",F8,"csch(",F9,"coth(",FA,"sech‾¹(",FB,"csch‾¹(",FC,"coth‾¹",FD
250.
Lbl F1           sec(
251. cos(θ)‾¹->θ
252. Goto θV
253.
Lbl F2           csc(
254. sin(θ)‾¹->θ
255. Goto θV
256.
Lbl F3           cot(
257. cos(θ)/sin(θ->θ
258. Goto θV
259.
Lbl F4           sec‾¹(
260. cos(θ‾¹->θ
261. Goto θV
262.
Lbl F5           csc‾¹(
263. sin(θ‾¹->θ
264. Goto θV
265.
Lbl F6           cot‾¹(
266. tan(θ‾¹->θ
267. Goto θV
268.
Lbl F8           sech(
269. cosh(θ)‾¹->θ
270. Goto θV
271.
Lbl F9           csch(
272. sinh(θ)‾¹->θ
273. Goto θV
274.
Lbl FA           coth(
275. cosh(θ)/sinh(θ->θ
276. Goto θV
277.
Lbl FB           sech‾¹(
278. {1,1}ln((1+√(1-^2))/->L2
279. DelVar θ
280. Goto θL
281.
Lbl FC           csch‾¹(
282. (θ<0)ln((1-√(1+θ^2))/θ)+(θ>0)ln((1+√(1-θ^2))/(θ->θ
283. Goto θV
284.
Lbl FD           coth‾¹
285. .5ln((θ+1)/(θ-1->θ
286. Goto θV
287.
Lbl G           Filter (sinc)
288. Prompt θ
289. (sin(θ)+(θ=0))/(θ+(θ=0->θ
290. Goto θV
291.
Lbl H           Euler (cis)
292. Prompt θ
293. cos(θ)+sin(θ->θ
294. Goto θV
295.
Lbl I           Sequences
296. Input "f(x)=?",Str2
297. StringEqu(Str2,Y
298. Prompt B,E,I
299. seq(Y,X,B,E,I->L2
300. DelVar Str2DelVar YDelVar BDelVar EDelVar IDelVar X
301. Goto θL
302.
Lbl J           Summation
303. Input "f(x)=?",Str2
304. StringEqu(Str2,Y
305. Prompt B,E,I
306. seq(Y,X,B,E,I->L2
307. sum(L2,1,dim(L2->θ
308. DelVar Str2DelVar YDelVar BDelVar EDelVar IDelVar XDelVar L2
309. Goto θV
310.
Lbl K           Product
311. Input "f(x)=?",Str2
312. StringEqu(Str2,Y
313. Prompt B,E,I
314. seq(Y,X,B,E,I->L2
315. prod(L2,1,dim(L2->θ
316. DelVar Str2DelVar YDelVar BDelVar EDelVar IDelVar XDelVar L2
317. Goto θV
318.
Lbl L           Limits
319. Prompt A,B
320. B/A->C
321. If abs(C)1
322. Then
323. DelVar ADelVar BDelVar CDelVar θ
324. Goto θV
325. Else
326. A/(1-C->θ
327. DelVar ADelVar BDelVar C
328. Goto θV
329.
Lbl M           Pascal's
330. Prompt N
331. N+1->dim(L2
332. For(I,0,N
333. N nCr I->L2(I+1
334. End
335. DelVar NDelVar I
336. Goto θL
337.
Lbl N           Fibonacci
338. Prompt F,T
339. (1+√(5))/2->P
340. T-F->dim(L2
341. For(N,F,T
342. (P&supN;-(1-P)^N)/√(5->L2(N-F+1
343. End
344. DelVar FDelVar TDelVar PDelVar N
345. Goto θL
346.
Lbl O           Phi ()
347. .5(1+√(5->θ
348. Goto θV
349.
Lbl P           Base converter
350. Input "ʟDIGITS=?",L2
351. Input "From B=?",B
352. Input "To B=?",C
353. sum(seq(L2(D)B^(dim(L2)-D),D,1,dim(L2)),1,dim(L2->N
354. {0->L3:1->Q
355. Repeat not(Q or R
356. int(N/C->Q
357. N-CQ->R:Q->N
358. If Q or R
359. R->L3(dim(L3)+1
360. End
361. seq(L3(D),D,dim(L3),1,¯ 1->L3
362. dim(L3)-1->dim(L3
363. L3->L2
364. DelVar L3DelVar BDelVar CDelVar DDelVar NDelVar QDelVar R
365. Goto θL
366.
Lbl Q           Dice
367. Prompt S,R
368. R->dim(L2
369. For(N,1,R
370. randInt(1,S->L2(N
371. End
372. DelVar SDelVar RDelVar N
373. Goto θL
374.
Lbl R           Digit count
375. Prompt N
376. 1+int(real(log(N->θ
377. DelVar N
378. Goto θV
379.
Lbl S           Sign
380. Prompt N
381. N/abs(N+(N=0->θ
382. DelVar N
383. Goto θV
384.
Lbl T           Bitwise logic
385. Prompt A,B
386. A->X:B->Y
387. DelVar O
388. Menu("OPERATION","A and B",S1,"A or B",S2,"A xor B",S3
389. Lbl S3:O+1->O
390. Lbl S2:O+1->O
391. Lbl S1:O+1->O
392. 1->C:DelVar θ
393. While A>0 or B>0
394. .5int(A->A
395. .5int(B->B
396. If O=1
397. fPart(A) and fPart(B->D
398. If O=2
399. fPart(A) or fPart(B->D
400. If O=3
401. fPart(A) xor fPart(B->D
402. θ+CD->θ:2C->C
403. End
404. X->A:Y->B
405. DelVar ADelVar BDelVar XDelVar YDelVar CDelVar ODelVar D
406. Goto θV
407. Lbl θV
408. Pause θ
409. Return
410. Lbl θL
411. Pause L2
412. Return
413. Lbl θM
414. Pause [B]
415. Return
416. Lbl θS
417. Pause Str2
418. Return
 
Reference:
Instructions: Click on the command name (in blue)to go to information on that command
Commands or Statements:
  augment( listA, listB)   Returns a list, which is list B appended to the end of list A
  ClrHome  clears home screen
  dim(  returns the dimension (number of elements) of list
  Disp  displays text or value specified
  End   Identifies end of For(, If-Then-Else, Repeat, or While loop.
  expr(  converts string to an expression
  Fix   sets fixed-decimal mode for number of decimal places
  Float  sets floating decimal mode. Displays decimal with no trailing zeros
  For (variable,begin,end[,increment]) :commands :End :commands :Executes commands through End, incrementing variable from begin by increment until variable end.
  Goto  goes to label specified. Goto requires a line label be implemented as a destination
  If condition :Then   :commands :End :commands: Executes commands from Then to End if condition = 1(true).
  If; Then; Else   : Executes commands from Then to Else If condition true: or from Else to End if condition false
  Input  prompts for value to store to variable. Requires user input through keypad.
  Int(  prompts for value to store to variable. Requires user input through keypad
  Lbl  creates a label of one or two characters
  Menu  generates a menu of up to seven items
  output( row, column)   displays text or value beginning at specified row and column
  Pause [value]   Displays value; suspends program execution until you press [ENTER]. Pause with value displays value on the current home screen. Value can be scrolled.
  round( value [,# decimals])  returns a number rounded to # decimals (=<9)
  seq( expression, variable, begin, end[, increment])   Returns list created by evaluating expression with regard to variable, from begin to end by increment
  SortA( listname) Sorts elements of listname in ascending (count up) order
  Str# (# is number)   String: A sequence of characters is called a string
  sum(  returns the sum of elements in list
  While condition   Executes commands while condition is true until end
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