Expression of type ExprTuple ¶

from the theory of proveit.numbers.summation ¶

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, ExprTuple, Lambda, i, j, k, x
from proveit.logic import And, Equals, Forall, InSet, NotEquals
from proveit.numbers import Add, Complex, Exp, Integer, Interval, LessEq, Sum, frac, one, subtract

# build up the expression from sub-expressions
expr = ExprTuple(Lambda(x, Conditional(Forall(instance_param_or_params = [j, k], instance_expr = Equals(Sum(index_or_indices = [i], summand = Exp(x, i), domain = Interval(j, k)), frac(subtract(Exp(x, j), Exp(x, Add(k, one))), subtract(one, x))), domain = Integer, condition = LessEq(j, k)), And(InSet(x, Complex), NotEquals(x, one)))))

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left(x \mapsto \left\{\forall_{j, k \in \mathbb{Z}~|~j \leq k}~\left(\left(\sum_{i = j}^{k} x^{i}\right) = \frac{x^{j} - x^{k + 1}}{1 - x}\right) \textrm{ if } x \in \mathbb{C} ,  x \neq 1\right..\right)

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	ExprTuple	1
1	Lambda	parameter: 62 body: 2
2	Conditional	value: 3 condition: 4
3	Operation	operator: 5 operand: 8
4	Operation	operator: 20 operands: 7
5	Literal
6	ExprTuple	8
7	ExprTuple	9, 10
8	Lambda	parameters: 58 body: 11
9	Operation	operator: 48 operands: 12
10	Operation	operator: 13 operands: 14
11	Conditional	value: 15 condition: 16
12	ExprTuple	62, 17
13	Literal
14	ExprTuple	62, 67
15	Operation	operator: 18 operands: 19
16	Operation	operator: 20 operands: 21
17	Literal
18	Literal
19	ExprTuple	22, 23
20	Literal
21	ExprTuple	24, 25, 26
22	Operation	operator: 27 operand: 34
23	Operation	operator: 29 operands: 30
24	Operation	operator: 48 operands: 31
25	Operation	operator: 48 operands: 32
26	Operation	operator: 33 operands: 58
27	Literal
28	ExprTuple	34
29	Literal
30	ExprTuple	35, 36
31	ExprTuple	61, 37
32	ExprTuple	66, 37
33	Literal
34	Lambda	parameter: 54 body: 39
35	Operation	operator: 64 operands: 40
36	Operation	operator: 64 operands: 41
37	Literal
38	ExprTuple	54
39	Conditional	value: 42 condition: 43
40	ExprTuple	44, 45
41	ExprTuple	67, 46
42	Operation	operator: 59 operands: 47
43	Operation	operator: 48 operands: 49
44	Operation	operator: 59 operands: 50
45	Operation	operator: 52 operand: 56
46	Operation	operator: 52 operand: 62
47	ExprTuple	62, 54
48	Literal
49	ExprTuple	54, 55
50	ExprTuple	62, 61
51	ExprTuple	56
52	Literal
53	ExprTuple	62
54	Variable
55	Operation	operator: 57 operands: 58
56	Operation	operator: 59 operands: 60
57	Literal
58	ExprTuple	61, 66
59	Literal
60	ExprTuple	62, 63
61	Variable
62	Variable
63	Operation	operator: 64 operands: 65
64	Literal
65	ExprTuple	66, 67
66	Variable
67	Literal

Expression of type ExprTuple¶

from the theory of proveit.numbers.summation¶

Expression of type ExprTuple ¶

from the theory of proveit.numbers.summation ¶