Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

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
import proveit
import proveit.numbers
from proveit import ExprTuple
from proveit.linear_algebra import ScalarMult, VecSum
from proveit.numbers import Exp, Interval, Mult, e, one, pi, two
from proveit.physics.quantum import Ket, ket1
from proveit.physics.quantum.QPE import _phase

# build up the expression from sub-expressions
expr = ExprTuple(VecSum(index_or_indices = [proveit.i], summand = ScalarMult(Exp(e, Mult(two, pi, proveit.numbers.i, _phase, proveit.i)), Ket(proveit.i)), domain = Interval(one, one)), ScalarMult(Exp(e, Mult(two, pi, proveit.numbers.i, _phase)), ket1))

expr:

# 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(\sum_{i=1}^{1} \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi \cdot i} \cdot \lvert i \rangle\right), \mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi} \cdot \lvert 1 \rangle\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions	expression
0	ExprTuple	1, 2
1	Operation	operator: 3 operand: 6
2	Operation	operator: 15 operands: 5
3	Literal
4	ExprTuple	6
5	ExprTuple	7, 8
6	Lambda	parameter: 38 body: 9
7	Operation	operator: 23 operands: 10
8	Operation	operator: 25 operand: 31
9	Conditional	value: 12 condition: 13
10	ExprTuple	29, 14
11	ExprTuple	31
12	Operation	operator: 15 operands: 16
13	Operation	operator: 17 operands: 18
14	Operation	operator: 32 operands: 19
15	Literal
16	ExprTuple	20, 21
17	Literal
18	ExprTuple	38, 22
19	ExprTuple	34, 35, 36, 37
20	Operation	operator: 23 operands: 24
21	Operation	operator: 25 operand: 38
22	Operation	operator: 27 operands: 28
23	Literal
24	ExprTuple	29, 30
25	Literal
26	ExprTuple	38
27	Literal
28	ExprTuple	31, 31
29	Literal
30	Operation	operator: 32 operands: 33
31	Literal
32	Literal
33	ExprTuple	34, 35, 36, 37, 38
34	Literal
35	Literal
36	Literal
37	Literal
38	Variable