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Expression of type Equals

from the theory of proveit.physics.quantum.QPE

In [1]:
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 e, l
from proveit.logic import Equals
from proveit.numbers import Exp, Interval, Sum, frac, one, subtract, two
from proveit.physics.quantum.QPE import _pos_domain, _two_pow__t_minus_one
In [2]:
# build up the expression from sub-expressions
sub_expr1 = [l]
expr = Equals(Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(subtract(l, one), two)), domain = _pos_domain), Sum(index_or_indices = sub_expr1, summand = frac(one, Exp(l, two)), domain = Interval(e, subtract(_two_pow__t_minus_one, one))))
expr:
In [3]:
# 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
In [4]:
# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())
\left(\sum_{l = e + 1}^{2^{t - 1}} \frac{1}{\left(l - 1\right)^{2}}\right) = \left(\sum_{l = e}^{2^{t - 1} - 1} \frac{1}{l^{2}}\right)
In [5]:
stored_expr.style_options()
namedescriptiondefaultcurrent valuerelated methods
operation'infix' or 'function' style formattinginfixinfix
wrap_positionsposition(s) at which wrapping is to occur; '2 n - 1' is after the nth operand, '2 n' is after the nth operation.()()('with_wrapping_at', 'with_wrap_before_operator', 'with_wrap_after_operator', 'without_wrapping', 'wrap_positions')
justificationif any wrap positions are set, justify to the 'left', 'center', or 'right'centercenter('with_justification',)
directionDirection of the relation (normal or reversed)normalnormal('with_direction_reversed', 'is_reversed')
In [6]:
# display the expression information
stored_expr.expr_info()
 core typesub-expressionsexpression
0Operationoperator: 1
operands: 2
1Literal
2ExprTuple3, 4
3Operationoperator: 6
operand: 8
4Operationoperator: 6
operand: 9
5ExprTuple8
6Literal
7ExprTuple9
8Lambdaparameter: 38
body: 10
9Lambdaparameter: 38
body: 12
10Conditionalvalue: 13
condition: 14
11ExprTuple38
12Conditionalvalue: 15
condition: 16
13Operationoperator: 19
operands: 17
14Operationoperator: 21
operands: 18
15Operationoperator: 19
operands: 20
16Operationoperator: 21
operands: 22
17ExprTuple51, 23
18ExprTuple38, 24
19Literal
20ExprTuple51, 25
21Literal
22ExprTuple38, 26
23Operationoperator: 41
operands: 27
24Operationoperator: 30
operands: 28
25Operationoperator: 41
operands: 29
26Operationoperator: 30
operands: 31
27ExprTuple32, 43
28ExprTuple33, 40
29ExprTuple38, 43
30Literal
31ExprTuple39, 34
32Operationoperator: 45
operands: 35
33Operationoperator: 45
operands: 36
34Operationoperator: 45
operands: 37
35ExprTuple38, 48
36ExprTuple39, 51
37ExprTuple40, 48
38Variable
39Variable
40Operationoperator: 41
operands: 42
41Literal
42ExprTuple43, 44
43Literal
44Operationoperator: 45
operands: 46
45Literal
46ExprTuple47, 48
47Literal
48Operationoperator: 49
operand: 51
49Literal
50ExprTuple51
51Literal