Expression of type Lambda ¶

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, 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 = 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())

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..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

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

Expression of type Lambda¶

from the theory of proveit.numbers.summation¶

Expression of type Lambda ¶

from the theory of proveit.numbers.summation ¶